From Jinshan: \u5f53\u5e74\u770b\u4e86\u300a\u6982\u7387\u8bba\u5bfc\u5f15\u300b\u4e4b\u540e\u5dee\u70b9\u53bb\u5b66\u6570\u5b66\u3002\u771f\u7684\u662f\u4f1f\u5927\u7684\u4eba\u548c\u4f1f\u5927\u7684\u4e66\u3002\u300a\u6982\u7387\u8bba\u5bfc\u5f15\u300b\u4e2d\u5b66\u751f\u5c31\u53ef\u4ee5\u770b\u61c2\u3002\u540c\u65f6\uff0c\u6700\u540e\u90e8\u5206\u5173\u4e8e\u4ec0\u4e48\u662f\u6570\u5b66\u80fd\u529b\u7684\u603b\u7ed3\uff0c\u5b8c\u5168\u53ef\u4ee5\u505a\u4e3a\u6570\u5b66\u5b66\u4ec0\u4e48\u6559\u4ec0\u4e48\u7684\u53c2\u8003\u3002\u4f1f\u5927\u7684\u4eba\u7684\u4f1f\u5927\u601d\u60f3\u5c31\u662f\u4e0d\u4e00\u6837\u3002\u540c\u65f6\u63a8\u8350\u770b\u770b\u53e6\u5916\u4e00\u4e2a\u5927\u6570\u5b66\u5bb6\u7684\u6559\u80b2\u601d\u60f3\uff1aWhitehead\u300a\u6559\u80b2\u7684\u76ee\u7684\u300b\u3002<\/p>\n
\u300aKolmogorov \u7684\u6578\u5b78\u89c0\u8207\u696d\u7e3e\u300b
\n\u4f0a\u85e4\u6e05<\/p>\n
\u5f53\u6211\u5f97\u77e5\u82cf\u8054\u4f1f\u5927\u7684\u6570\u5b66\u5bb6\uff0c84\u5c81\u7684\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b(Andreyii Nikolaevich Kolmogorov)\u6559\u6388\u4e8e1987\u5e7410\u670820\u65e5\u79bb\u5f00\u4eba\u4e16\u65f6\uff0c\u6211\u611f\u5230\u50cf\u662f\u5931\u53bb\u4e86\u652f\u67f1\u90a3\u6837\u60b2\u54c0\u4e0e\u5b64\u5bc2\u3002\u5728\u6211\u8fd8\u662f\u5b66\u751f\u65f6\uff081937\u5e74\uff09\u8bfb\u4e86\u4ed6\u7684\u540d\u8457\u300a\u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5\u300b\u4e4b\u540e\uff0c\u4fbf\u7acb\u5fd7\u94bb\u7814\u6982\u7387\u8bba\uff0c\u5e76\u6301\u7eed\u4e8650\u5e74\u4e4b\u4e45\u3002\u5bf9\u4e8e\u6211\u6765\u8bf4\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5c31\u662f\u6211\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n
\u6211\u4e0e\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u6559\u6388\u4ec5\u4f1a\u8fc73\u6b21\u9762\u3002\u7b2c\u4e00\u6b21\u662f1962\u5e74\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a(\u4e8e\u745e\u5178\u9996\u90fd\u65af\u5fb7\u54e5\u5c14\u6469\u53ec\u5f00)\u65f6\uff0c\u5f00\u5e55\u5f0f\u524d\u6211\u5728\u5927\u5385\u91cc\u6f2b\u6b65\u3002\u5f53\u542c\u89c1\u201cIto\u201d\u7684\u4eb2\u5207\u7684\u62db\u547c\u58f0\u65f6\uff0c\u6211\u53c8\u60ca\u53c8\u559c\u3002\u4ed6\u7528\u5fb7\u8bed\u95ee\u5230\u201c\u4f60\u591a\u5927\u5e74\u9f84\uff1f\u201d\u6211\u7b54\u9053\uff1a\u201cSeibenundvierzig.\u201d\u4ed6\u518d\u95ee\uff1a\u201cDreiBig?\u201d\uff08\u4e09\u5341\u51e0\uff1f\uff09\u5927\u6982\u65e5\u672c\u4eba\u90fd\u663e\u5f97\u5e74\u8f7b\uff0c\u6211\u4e5f\u8bb8\u88ab\u770b\u5f97\u5e74\u8f7b\u4e8610\u5c81\u3002\u53c8\u8fc7\u4e86\u4e8c\u4e09\u65e5\uff0cH.Cramer\u6559\u6388\uff08\u5168\u745e\u5178\u7684\u5927\u5b66\u6821\u957f(Chancelor)\uff0c\u6982\u7387\u8bba\u3001\u89e3\u6790\u6570\u8bba\u7684\u4e13\u5bb6\uff09\u5728\u5bb6\u91cc\u4e3e\u884c\u4e86\u665a\u9910\u4f1a\uff0c\u62db\u5f85\u51fa\u5e2d\u4f1a\u8bae\u7684\u5927\u7ea610\u540d\u6709\u5173\u6982\u7387\u65b9\u9762\u7684\u5b66\u8005\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b,J.L.Doob\u4e0e\u6211\u90fd\u5728\u5176\u4e2d\u3002<\/p>\n
\u7b2c\u4e8c\u6b21\u662f1978\u5e74\uff0c\u5728\u53c2\u52a0\u4e86\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\uff08\u4e8e\u82ac\u5170\u9996\u90fd\u8d6b\u5c14\u8f9b\u57fa\u53ec\u5f00\uff09\u4e4b\u540e\uff0c\u6211\u53c8\u51fa\u5e2d\u4e86\u6982\u7387\u7edf\u8ba1\u56fd\u9645\u5b66\u672f\u8ba8\u8bba\u4f1a(Vilnius,Lihtuania,\u524d\u82cf\u8054)\uff0c\u56de\u56fd\u9014\u4e2d\uff0c\u8def\u7ecf\u83ab\u65af\u79d1\u65f6\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u62db\u5f85Varadhan(\u7ebd\u7ea6\u5927\u5b66\u67ef\u6717\u7814\u7a76\u6240)\u3001Prokhorov\uff08\u82cf\u8054\u79d1\u5b66\u9662\uff09\u548c\u6211\u5728\u514b\u91cc\u59c6\u6797\u5bab\u65c1\u7684\u4e00\u5ea7\u9ad8\u96c5\u7684\u9910\u5385\u5403\u4e86\u5348\u9910\u3002\u5f53\u65f6\u5df2\u542c\u8bf4\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5bf9\u9ad8\u4e2d\u7684\u6570\u5b66\u6559\u80b2\u5f88\u70ed\u5fc3\uff0c\u62db\u6536\u4e86\u4e00\u4e9b\u4f18\u79c0\u7684\u5b66\u751f\uff0c\u4eb2\u81ea\u5f00\u8bfe\u6559\u6388\u3002\u6211\u4fbf\u8be2\u95ee\u4e86\u5176\u5185\u5bb9\u3002\u4ed6\u4e3e\u4f8b\u8bf4\uff1a\u6bd4\u5982\u5411\u5b66\u751f\u5c55\u793a\u7b80\u5355\u7684\u5411\u91cf\u573a\uff08\u901f\u5ea6\u573a\uff09\u7684\u56fe\uff0c\u5e76\u8981\u6c42\u4ed6\u4eec\u753b\u51fa\u79ef\u5206\u66f2\u7ebf\uff08\u8f68\u8ff9\uff09\uff1b\u53c8\u5982\u8ba9\u5b66\u751f\u8003\u8651\u5177\u4f53\u7684\u5206\u679d\u8fc7\u7a0b\u7684\u95ee\u9898\u7b49\u7b49\uff0c\u4ee5\u57f9\u517b\u5b66\u751f\u7684\u6570\u5b66\u76f4\u89c2\u80fd\u529b\u3002
\n\u7b2c\u4e09\u6b21\u662f1983\u5e74\u5728Tbilisi(Georgia,\u524d\u82cf\u8054)\u53ec\u5f00\u7684\u65e5\u82cf\u6982\u7387\u7edf\u8ba1\u5b66\u672f\u8ba8\u8bba\u4f1a\u4e0a\u3002\u5f53\u65f6\uff0c\u5c3d\u7ba1\u4ed6\u7684\u5065\u5eb7\u72b6\u51b5\u4e0d\u5927\u597d\uff0c\u4ecd\u7136\u4f5c\u4e86\u8bb2\u6f14\uff0c\u5e76\u5728\u5bb4\u4f1a\u4e0a\u52aa\u529b\u521b\u9020\u6d3b\u8dc3\u7684\u6c14\u6c1b\u3002\u663e\u7136\u5e74\u8f7b\u7684\u4e00\u4ee3\u662f\u5f88\u5d07\u656c\u4ed6\u7684\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5728\u6570\u5b66\u7684\u51e0\u4e4e\u6240\u6709\u9886\u57df\u4e2d\uff0c\u90fd\u63d0\u51fa\u4e86\u72ec\u521b\u7684\u601d\u60f3\uff0c\u5bfc\u5165\u4e86\u5d2d\u65b0\u7684\u65b9\u6cd5\uff0c\u4ed6\u7684\u4e1a\u7ee9\u662f\u975e\u5e38\u8f89\u714c\u7684\u3002\u7136\u800c\uff0c\u6211\u89c1\u5230\u4ed6\u65f6\u7ed9\u6211\u7559\u4e0b\u7684\u5370\u8c61\u5374\u662f\u4e0d\u4fee\u8fb9\u5e45\u7684\u6e29\u539a\u7684\u541b\u5b50\u5f62\u8c61\uff0c\u8fd9\u4e5f\u8bb8\u6b63\u662f\u4f1f\u5927\u6570\u5b66\u5bb6\u7684\u5f62\u8c61\u5427\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u8bba\u6587\u6211\u81ea\u8ba4\u4e3a\u57fa\u672c\u4e0a\u90fd\u597d\u597d\u5730\u8bfb\u8fc7\u4e86\uff0c\u5728\u64b0\u5199\u672c\u7a3f\u65f6\uff0c\u6211\u53c8\u5bf9\u4ed6\u6574\u4e2a\u7684\u7814\u7a76\u6210\u679c\u505a\u4e86\u4e00\u4e2a\u76f4\u63a5\u6216\u95f4\u63a5\u7684\u8c03\u67e5\u3002\u5bf9\u5176\u7814\u7a76\u7684\u5e7f\u5ea6\u548c\u6df1\u5ea6\u4e0d\u5f97\u4e0d\u53f9\u670d\u3002\u7531\u4e8e\u65f6\u95f4\u548c\u7bc7\u5e45\u7684\u9650\u5236\uff0c\u6211\u4ec5\u5411\u8bfb\u8005\u8c08\u4e00\u4e9b\u5e76\u4e0d\u5168\u9762\u7684\u81ea\u5df1\u7684\u611f\u53d7\u3002<\/p>\n
\u5409\u6cfd\u5c1a\u660e\uff08\u4eac\u90fd\u5927\u5b66\uff09\u3001\u6c60\u7530\u4fe1\u884c\uff08\u5927\u962a\u5927\u5b66\uff09\u4e8c\u4f4d\u6559\u6388\u53ca\u4eac\u90fd\u5927\u5b66\u6570\u7406\u7814\u56fe\u4e66\u5ba4\u7684\u5404\u4f4d\u5e2e\u52a9\u6211\u67e5\u627e\u4e86\u8d44\u6599\uff0c\u5728\u6b64\u6211\u8868\u793a\u8877\u5fc3\u7684\u611f\u8c22\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7b80\u5386
\n\u6839\u636eB.V.Gnedenko\u5728\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b70\u5bff\u8fb0\u65f6\u7684\u8bb2\u6f14\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u4e8e1903\u5e74\u8bde\u751f\u4e8e\u4fc4\u7f57\u65af\u7684\u6751\u9547\uff08\u73b0\u5728\u4e3a\u5e02\uff09Tambov\u3002\u7236\u4eb2\u662f\u519c\u5b66\u5bb6\uff0c\u6bcd\u4eb2\u5728\u751f\u4e0b\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u540e\u4e0d\u4e45\u4fbf\u79bb\u5f00\u4eba\u4e16\uff0c\u4ed6\u662f\u88ab\u53d4\u6bcd\u7b49\u629a\u517b\u957f\u5927\u7684\u30021920\u5e74\uff0817\u5c81\uff09\u8fdb\u5165\u83ab\u65af\u79d1\u5927\u5b66\u4e4b\u524d\uff0c\u4ed6\u5f53\u8fc7\u5217\u8f66\u4e0a\u7684\u4e58\u52a1\u5458\uff0c\u4e1a\u4f59\u65f6\u95f4\u5199\u4e86\u5173\u4e8e\u725b\u987f\u529b\u5b66\u5b9a\u5f8b\u7684\u8bba\u6587\uff0c\u8bba\u6587\u7684\u539f\u7a3f\u672a\u80fd\u4fdd\u5b58\u4e0b\u6765\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\u4ed6\u662f\u591a\u4e48\u65e9\u719f\u7684\u5929\u624d\u3002\u90a3\u65f6\uff0c\u4fc4\u56fd\u9769\u547d\uff081917\uff09\u5df2\u7ecf\u7206\u53d1\uff0c\u6211\u5f88\u60f3\u77e5\u9053\u4ed6\u5f53\u65f6\u6240\u5904\u7684\u73af\u5883\uff0c\u5f88\u9057\u61be\u6ca1\u6709\u6709\u5173\u7684\u8d44\u6599\u3002<\/p>\n
1920\u5e74\u8fdb\u5165\u83ab\u65af\u79d1\u5927\u5b66\uff0c\u6700\u521d\u5bf9\u4fc4\u56fd\u7684\u5386\u53f2\u611f\u5174\u8da3\uff0c\u8fd8\u8c03\u67e5\u4e8615\uff5e16\u4e16\u7eaa\u7684\u8bfa\u5e03\u54e5\u7f57\u5fb7\u7684\u8d22\u4ea7\u767b\u8bb0\u3002\u4ee5\u540e\u53c2\u52a0\u4e86V.V.Stepanov\u7684\u5085\u91cc\u53f6\u7ea7\u6570\u8ba8\u8bba\u73ed\uff0c\u5e76\u4e8e1922\u5e74\uff0819\u5c81\uff09\u5199\u51fa\u4e86\u5173\u4e8e\u5085\u91cc\u53f6\u7ea7\u6570\uff0c\u89e3\u6790\u96c6\u5408\u7684\u8457\u540d\u8bba\u6587\uff0c\u9707\u52a8\u4e86\u5b66\u672f\u754c\u3002\u5176\u540e\u72b9\u5982\u5929\u9a6c\u884c\u7a7a\uff0c\u8fde\u7eed\u53d1\u8868\u4e86\u8bb8\u591a\u91cd\u8981\u7684\u7814\u7a76\u6210\u679c\u30021925\u5e74\u83ab\u65af\u79d1\u5927\u5b66\u6bd5\u4e1a\uff0c1931\u5e74\u5f53\u5927\u5b66\u6559\u6388\uff0c1933\u5e74\u4efb\u5927\u5b66\u6570\u5b66\u7814\u7a76\u6240\u6240\u957f\uff0c1937\u5e74\u6210\u4e3a\u82cf\u8054\u79d1\u5b66\u9662\u9662\u58eb\u3002\u81f31987\u5e74\u901d\u4e16\u6b62\uff0c\u5bf9\u6570\u5b66\u7684\u7814\u7a76\u6559\u80b2\u4f5c\u51fa\u4e86\u5f88\u591a\u91cd\u5927\u7684\u8d21\u732e\u3002
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u89c2
\n\u4e86\u89e3\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u89c2\u7684\u6700\u597d\u7684\u8d44\u6599\uff0c\u5927\u6982\u8981\u5c5e\u82cf\u8054\u5927\u767e\u79d1\u8f9e\u5178\u4e2d\u4ed6\u6240\u6267\u7b14\u7684\u201c\u6570\u5b66\u201d\u90e8\u5206\u5427\u3002\u5df2\u7ecf\u51fa\u4e86\u82f1\u6587\u7248\uff0c\u6211\u8bfb\u4e86\u82f1\u6587\u7248\uff0c\u4e0e\u539f\u6587\uff08\u4fc4\u8bed\uff09\u6bd4\u8f83\uff0c\u82f1\u6587\u7248\u7a0d\u5fae\u7f29\u7565\u4e86\u4e00\u4e9b\uff0c\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u4ed6\u5148\u9610\u8ff0\u4e86\u5176\u6570\u5b66\u89c2\uff0c\u7136\u540e\u901a\u8ff0\u4e86\u81ea\u53e4\u81f3\u4eca\u7684\u6570\u5b66\u53f2\uff0c\u5e76\u4e14\u4ece\u4ed6\u7684\u6570\u5b66\u89c2\u51fa\u53d1\uff0c\u8be6\u7ec6\u63cf\u8ff0\u4e86\u8fd9\u4e2a\u5386\u53f2\u7684\u5404\u4e2a\u9636\u6bb5\uff0c\u5b83\u53ef\u4ee5\u8bf4\u662f\u4e3a\u6570\u5b66\u5bb6\u3001\u79d1\u5b66\u5bb6\u4eec\u6240\u5199\u7684\u6570\u5b66\u53f2\u3002\u6211\u9976\u6709\u5174\u8da3\u5730\u4e00\u53e3\u6c14\u8bfb\u5b8c\u4e86\u5168\u7bc7\u3002\u8981\u8bf4\u660e\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u89c2\uff0c\u4e0d\u4ec5\u5e94\u5f53\u770b\u8fd9\u7bc7\u6587\u7ae0\u7684\u5f00\u59cb\u90e8\u5206\uff0c\u4e5f\u5e94\u5f53\u53c2\u7167\u5360\u8be5\u6587\u5927\u90e8\u5206\u7684\u6570\u5b66\u53f2\uff0c\u4f46\u7531\u4e8e\u7bc7\u5e45\u53ca\u65f6\u95f4\u7684\u9650\u5236\uff0c\u6211\u4ec5\u5c06\u6587\u7ae0\u7684\u5f00\u59cb\u90e8\u5206\u7b80\u8981\u4ecb\u7ecd\u5982\u4e0b\u3002<\/p>\n
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(1)\u56e0\u6b64\u6570\u5b66\u7684\u7814\u7a76\u5bf9\u50cf\u662f\u4ea7\u751f\u4e8e\u73b0\u5b9e\u4e2d\u7684\u3002\u7136\u800c\u4f5c\u4e3a\u6570\u5b66\u52a0\u4ee5\u7814\u7a76\u65f6\uff0c\u5fc5\u987b\u79bb\u5f00\u73b0\u5b9e\u7684\u7d20\u6750\uff08\u6570\u5b66\u7684\u62bd\u8c61\u6027\uff09\u3002<\/p>\n
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\u603b\u4e4b\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u89c2\u662f\u7531\u4ed6\u7684\u6570\u5b66\u4e0a\u7684\u72ec\u521b\u6027\uff0c\u5bf9\u4e8e\u6570\u5b66\u5e94\u7528\u6240\u62b1\u6709\u7684\u6fc0\u60c5\u53ca\u5bf9\u4e8e\u6570\u5b66\u53d1\u5c55\u7684\u5386\u53f2\u6240\u5177\u6709\u7684\u6d1e\u5bdf\u3002\u8fd9\u51e0\u4e2a\u65b9\u9762\u6240\u7ec4\u6210\u7684\uff0c\u96be\u4ee5\u7528\u4e00\u8a00\u6765\u6982\u4e4b\u3002\u5982\u679c\u4e00\u5b9a\u8981\u7528\u4e00\u53e5\u8bdd\u6765\u603b\u7ed3\uff0c\u4e5f\u8bb8\u53ef\u4ee5\u8fd9\u6837\u8bf4\uff1a\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u628a\u6570\u5b66\u770b\u6210\u4e3a\u53ef\u4ee5\u65e0\u9650\u5236\u5730\u6210\u957f\u7684\u201c\u751f\u7269\u4f53\u201d\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u4e1a\u7ee9
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5199\u4e86\u4e0a\u767e\u7bc7\u8bba\u6587\uff0c\u4ece\u4e2d\u53ef\u4ee5\u770b\u51fa\u5176\u7279\u70b9\u662f\uff1a\u201c\u5e7f\u6cdb\u7684\u7814\u7a76\u9886\u57df\u201d\u3001\u201c\u5f15\u5165\u65b0\u89c2\u70b9\u7684\u72ec\u521b\u6027\u201d\u53ca\u201c\u660e\u5feb\u7684\u53d9\u8ff0\u201d\uff0c\u5176\u7814\u7a76\u9886\u57df\u5305\u62ec\u5b9e\u53d8\u51fd\u6570\u8bba\u3001\u6570\u5b66\u57fa\u7840\u8bba\u3001\u62d3\u6251\u7a7a\u95f4\u8bba\u3001\u6cdb\u51fd\u5206\u6790\u3001\u6982\u7387\u8bba\u3001\u52a8\u6001\u7cfb\u7edf\u3001\u7edf\u8ba1\u529b\u5b66\u3001\u6570\u7406\u7edf\u8ba1\u3001\u4fe1\u606f\u8bba\u7b49\u591a\u4e2a\u5206\u652f\u3002\u4e0b\u9762\u7ed3\u5408\u80cc\u666f\u6982\u8ff0\u4e00\u4e0b\u8fd9\u4e9b\u7814\u7a76\u3002<\/p>\n
\u5b9e\u53d8\u51fd\u6570\u8bba
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5728\u83ab\u65af\u79d1\u5927\u5b66\u8bfb\u4e66\u65f6\u53c2\u52a0\u4e86Stepanov\u7684\u5085\u91cc\u53f6\u7ea7\u6570\u8ba8\u8bba\u73ed\uff0c\u4ece\u90a3\u65f6\uff081921\uff09\u5f00\u59cb\uff0c\u4ed6\u5bf9\u6570\u5b66\u4ea7\u751f\u4e86\u4e0e\u8da3\u3002\u5f53\u65f6\uff0c\u4e3b\u8981\u7814\u7a76\u8fde\u7eed\u51fd\u6570\u7684\u5fae\u79ef\u5206\u5b66\u6b63\u5728\u5411\u7814\u7a76\u53ef\u6d4b\u51fd\u6570\u7684\u5b9e\u53d8\u51fd\u6570\u8bba\u53d1\u5c55\u3002\u8fd9\u4e00\u65b0\u7684\u6570\u5b66\u9886\u57df\u53d7\u5230\u4e86\u6781\u5927\u7684\u5173\u6ce8\u3002\u4ed6\u4e8e1922\u5e74\uff0819\u5c81\uff09\u65f6\uff0c\u901a\u8fc7\u5f15\u5165\u96c6\u5408\u6f14\u7b97\uff0c\u8bc1\u660e\u4e86\u5305\u542b\u201cBorel\u4e0d\u53ef\u6d4b\u89e3\u6790\u96c6\u5408\u7684\u5b58\u5728\u5b9a\u7406\u201d\u7684\u65b0\u7684\u5b9a\u7406\u3002\u540c\u5e74\uff0c\u4ed6\u8fd8\u6210\u529f\u5730\u7814\u7a76\u4e86\u201c\uff08\u5f62\u5f0f\u4e0a\uff09\u5085\u91cc\u53f6\u7ea7\u6570\u5728\u51e0\u4e4e\u6240\u6709\u70b9\u4e0a\uff08\u4ee5\u540e\u53c8\u7814\u7a76\u4e86\u6240\u6709\u70b9\u4e0a\uff09\u53d1\u6563\u7684\u53ef\u79ef\u51fd\u6570\u7684\u6784\u6210\u201d\u3002\u5173\u4e8e\u5085\u91cc\u53f6\u7ea7\u6570\u3001\u6b63\u4ea4\u51fd\u6570\u7684\u5c55\u5f00\uff0c\u4ed6\u4e5f\u5199\u4e86\u51e0\u7bc7\u8bba\u6587\u3002\u4ed6\u8fd8\u5c1d\u8bd5\u4e86\u52d2\u8d1d\u683c\uff08Lebesgue\uff09\u79ef\u5206\u7684\u63a8\u5e7f\uff0c\u6d89\u53ca\u4e86Denjoy\u79ef\u5206\u7684\u7814\u7a76\u3002\u8fd9\u4e9b\u5927\u4f53\u4e0a\u662f1930\u5e74\u4ee5\u524d\u7684\u7814\u7a76\u5de5\u4f5c\u3002<\/p>\n
\u6982\u7387\u8bba\u57fa\u7840
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\n\uff08\u5e03\u6717\u8fd0\u52a8\uff09\u5df2\u7ecf\u505a\u8fc7\u5c1d\u8bd5\u3002\u4f46\u7528\u8fd9\u4e2a\u65b9\u6cd5\u6765\u5bf9\u5f85\u6240\u6709\u95ee\u9898\u7684\u662f\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u300a\u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5\u300b\u3002\u4ed6\u8bc1\u660e\u4e86\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\u53ef\u4ee5\u6709\u76ee\u7684\u5730\u6784\u9020\u51faP\u7684\u5b9a\u7406\uff0c\u8fd9\u5c31\u662f\u8457\u540d\u7684\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u6269\u5f20\u5b9a\u7406\u3002<\/p>\n
\u8fc7\u53bb\u4f5c\u4e3a\u5177\u4f53\u7684\u6d4b\u5ea6\u4e00\u822c\u4ec5\u8003\u8651Lebesgue-Stieltjes\u6d4b\u5ea6\u548cLie\u7fa4\u4e0a\u7684\u4e0d\u53d8\u6d4b\u5ea6\u3002\u7531\u4e8e\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6d4b\u5ea6\u8bba\u5f0f\u7684\u6982\u7387\u8bba\uff0c\u65b0\u578b\u7684\u6982\u7387\u6d4b\u5ea6\u53ca\u6709\u5173\u7684\u65b0\u95ee\u9898\u5728\u5bf9\u5076\u7136\u73b0\u8c61\u7684\u6570\u5b66\u7814\u7a76\u4e2d\u4e0d\u65ad\u5730\u4ea7\u751f\u4e86\u51fa\u6765\u3002
\n\u6982\u7387\u8bba
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u53d7\u5230\u8f9b\u94a6\uff08A.Y.Khinchin\uff09\u7684\u5f71\u54cd\uff0c1925\u5e74\u524d\u540e\u5f00\u59cb\u7814\u7a76\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u7684\u7ea7\u6570\u7684\u6536\u655b\u95ee\u9898\u53ca\u53d1\u6563\u65f6\u7684\u9636\u6570\u3002\u6309\u7740\u7814\u7a76\u4e86\u7ef4\u7eb3\uff08Wiener\uff09\u8fc7\u7a0b\uff0c\u5728\u8fd9\u4e9b\u7814\u7a76\u4e2d\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5f15\u5165\u4e86\u51e0\u4e2a\u65b0\u7684\u601d\u60f3\u548c\u65b9\u6cd5\uff0c\u5176\u4e2dKolmogorov0-1\u5f8b\u3001Kolmogorov\u4e0d\u7b49\u5f0f\uff0cKhinchin-Kolmogorov\u4e09\u7ea7\u6570\u5b9a\u7406\uff0cKolmogorov\u5f3a\u5927\u6570\u5f8b\uff0cKolmogorov\u5224\u522b\u6cd5\uff0cKolmogorov\u8c31\uff08\u6e4d\u6d41\uff09\u7b49\u662f\u7279\u522b\u8457\u540d\u7684\u30021939\u5e74\u4ed6\u8fd8\u5c06\u5f31\u5e73\u7a33\u8fc7\u7a0b\u7684\u5185\u63d2\u3001\u5916\u63a8\u95ee\u9898\u5f52\u7ed3\u4e3a\u5085\u91cc\u53f6\u5206\u6790\u7684\u95ee\u9898\u800c\u4e00\u4e3e\u89e3\u51b3\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u8fd8\u5c06\u52a8\u6001\u7cfb\u7edf\u5206\u4e3a\u51b3\u5b9a\u8bba\u7684\uff08\u53e4\u5178\u7684\uff09\u52a8\u6001\u7cfb\u7edf\u548c\u6982\u7387\u8bba\u7684\u52a8\u6001\u7cfb\u7edf\uff08\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\uff09\uff0c\u63cf\u8ff0\u524d\u8005\u8f68\u9053\u7684\u662f\u5e38\u5fae\u5206\u65b9\u7a0b\uff0c\u800c\u51b3\u5b9a\u540e\u8005\u8f6c\u79fb\u6982\u7387\u7684\u662f\u629b\u7269\u578b\u504f\u5fae\u5206\u65b9\u7a0b\uff0c\u5373\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5f15\u5165\u7684\u5411\u524d\u65b9\u7a0b\u5e8f\u548c\u5411\u540e\u65b9\u7a0b\u5f0f\uff08\u3008\u5173\u4e8e\u6982\u7387\u8bba\u4e2d\u7684\u5206\u6790\u65b9\u6cd5\u3009\uff0cMath.Ann.1931\uff09\u3002\u5728\u90a3\u4ee5\u524d\uff0c\u6982\u7387\u8bba\uff08\u6cdb\u51fd\u5206\u6790\uff09\u4e5f\u5f00\u59cb\u5f97\u5230\u5e94\u7528\uff0c\u6982\u7387\u8bba\u7684\u5185\u5bb9\u53d8\u5f97\u6781\u5176\u4e30\u5bcc\u8d77\u6765\u30021950\u5e74\u4ee3\u7684\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u7684\u663e\u8457\u53d1\u5c55\u7684\u6e90\u6cc9\u5c31\u662f\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u8fd9\u4e2a\u7814\u7a76\u3002\u6211\u4ece\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u8fd9\u7bc7\u8bba\u6587\u7684\u5e8f\u8a00\u4e2d\u7684\u601d\u60f3\u5f97\u5230\u542f\u53d1\uff0c\u5f15\u5165\u4e86\u8868\u73b0\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u7684\u8f68\u9053\u7684\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u5f0f\u3002\u8fd9\u4e5f\u51b3\u5b9a\u4e86\u6211\u4ee5\u540e\u7684\u7814\u7a76\u7684\u65b9\u5411\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u300c\u57fa\u672c\u6982\u5ff5\u300d\u548c\u300c\u5206\u6790\u65b9\u6cd5\u300d\u5bf9\u6211\u6765\u8bf4\u53ef\u8c13\u81f3\u5b9d\u3002<\/p>\n
\u6570\u7406\u7edf\u8ba1
\n\u5728\u65e5\u672c\u5f88\u9057\u61be\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u4e4b\u95f4\u7684\u4ea4\u6d41\u4e0d\u592a\u6d3b\u8dc3\uff0c\u800c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7b49\u82cf\u8054\u7684\u6982\u7387\u8bba\u4e13\u5bb6\u662f\u975e\u5e38\u91cd\u89c6\u4e8c\u8005\u7684\u5173\u7cfb\u7684\u3002\u6982\u7387\u8bba\u662f\u4ee5\u6982\u7387\u7a7a\u95f4\u4e3a\u57fa\u7840\u7684\uff0c\u5728\u5e94\u7528\u4e8e\u73b0\u5b9e\u95ee\u9898\u7684\u65f6\u5019\uff0c\u9700\u8981\u8003\u8651\u82e5\u5e72\u6982\u7387\u7a7a\u95f4\uff0c\u7136\u540e\u51b3\u5b9a\u54ea\u4e2a\u662f\u6700\u9002\u5408\u4e8e\u5b9e\u9645\u95ee\u9898\u7684\u6982\u7387\u6a21\u5f0f\u3002\u8fd9\u4e2a\u51b3\u5b9a\u53ef\u4ee5\u8bf4\u662f\u6570\u7406\u7edf\u8ba1\u5b66\u7684\u4e00\u4e2a\u76ee\u7684\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u4e5f\u5199\u4e86\u4e0d\u5c11\u6570\u7406\u7edf\u8ba1\u5b66\u7684\u8bba\u6587\u3002\u5728\u975e\u53c2\u6570\u68c0\u9a8c\u6cd5\u4e2d\u7528\u5230\u7684Kolmogorov-Smirnov\u5b9a\u7406\u662f\u5f88\u6709\u540d\u7684\u3002<\/p>\n
\u6570\u5b66\u57fa\u7840\u8bba
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u4ece\u5e74\u8f7b\u65f6\u8d77\uff0c\u5c31\u5bf9\u6570\u5b66\u57fa\u7840\u8bba\uff0c\u7279\u522b\u662fBrouwer\u7684\u76f4\u89c2\u4e3b\u4e49\uff08\u6709\u9650\u7acb\u573a\uff09\u6709\u7740\u6d53\u539a\u7684\u5174\u8da3\uff08\u4f8b\u5982\u300aMath.Zeit.\u300b,35(1932),58-65\uff09\uff0c\u5173\u4e8e\u7b97\u6cd5\u4ed6\u4e5f\u4f5c\u4e86\u7814\u7a76\u3002<\/p>\n
\u62d3\u6734\u7a7a\u95f4\u8bba\u548c\u51fd\u6570\u7a7a\u95f4\u8bba\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u548cJ.W.Alexander\u5171\u540c\u5f00\u521b\u4e86\u4e0a\u540c\u8c03\u7406\u8bba\uff0c\u8fd9\u662f\u4f17\u6240\u5468\u77e5\u7684\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u8fd8\u662f\u540c\u65f6\u5177\u6709\u62d3\u6251\u7ed3\u6784\u548c\u4ee3\u6570\u7ed3\u6784\u7684\u7a7a\u95f4\u7406\u8bba\uff08\u7ebf\u6027\u62d3\u6251\u7a7a\u95f4\u3001\u62d3\u6251\u73af\uff09\u7814\u7a76\u7684\u5f00\u521b\u8005\u4e4b\u4e00\u3002<\/p>\n
\u4ed6\u8fd8\u7814\u7a76\u4e86\u5168\u6709\u754c\u7684\u8ddd\u79bb\u7a7a\u95f4E\u7684\u03b5-\u7f51\u4e2d\u6700\u5c0f\u53ef\u80fd\u7684\u70b9\u6570\u5f53\u65f6\u7684\u6027\u72b6\uff0c\u4f5c\u4e3aE\u7684\u7279\u5f81\u91cf\u5f15\u5165\u4e86\u03b5-\u71b5\u3001\u03b5-\u5bb9\u91cf\u7684\u6982\u5ff5\u3002\u5c06\u5176\u5e94\u7528\u4e8eE\u4e3a\u8fde\u7eed\u51fd\u6570\u7a7a\u95f4\u7684\u5b50\u7a7a\u95f4\u7684\u60c5\u5f62\u3014\u4e0eV.M.Tikhomirov\u5408\u8457\uff0cUspehi
\n(1959)\u3015\u3002\u8fd9\u662f\u6cdb\u51fd\u5206\u6790\u65b9\u9762\u7684\u5d2d\u65b0\u7684\u89c2\u70b9\u3002
\n\u52a8\u6001\u7cfb\u7edf<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5bf9\u4e8e\u53e4\u5178\u52a8\u6001\u7cfb\u7edf\u6709\u7740\u5f88\u6df1\u7684\u77e5\u8bc6\uff0c\u4ed6\u5199\u8fc7\u51e0\u7bc7\u91cd\u8981\u7684\u8bba\u6587\uff08\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u8bba\u6587\u96c6,1954,Amsterdam,1,315-333\uff09\u3002\u4ed6\u8fd8\u7814\u7a76\u4e86\u4e00\u822c\u7684\u52a8\u6001\u7cfb\u7edf\uff0c\u5f15\u5165\u4e86\u201cKolmogorov\u6d41\u201d\u7684\u6982\u5ff5\u3002\u4f5c\u4e3a\u6d41\u7684\u7279\u5f81\u91cf\uff0c\u5927\u5bb6\u77e5\u9053\u6709\u8c31\u578b(Hellinger-Hahn)\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u53c8\u5f15\u5165\u4e86\u71b5\u8fd9\u4e2a\u65b0\u7684\u7279\u5f81\u91cf\u3002\u6beb\u65e0\u7591\u95ee\uff0c\u8fd9\u4e5f\u4e3a\u65b0\u7684\u904d\u5386\u7406\u8bba\u5f00\u8f9f\u4e86\u9053\u8def\u3002<\/p>\n
\u5728\u5176\u5b83\u65b9\u9762\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u4e5f\u4f5c\u4e86\u8bb8\u591a\u6709\u540d\u7684\u7814\u7a76\u5de5\u4f5c\u3002\u4f8b\u5982\u5e0c\u5c14\u4f2f\u7279\u7684\u7b2c13\u95ee\u9898\u7684\u5426\u5b9a\u6027\u89e3\u51b3\uff0c\u968f\u673a\u6570\u8868\u7684\u8003\u5bdf\uff0c\u4ee5\u53ca\u5173\u4e8e\u4fe1\u606f\u8bba\u7684\u7814\u7a76\u7b49\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u6559\u80b2\u89c2
\n\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5728\u83ab\u65af\u79d1\u5927\u5b66\u57f9\u517b\u4e86\u8bb8\u591a\u6570\u5b66\u5bb6\uff0c\u5176\u4e2d\u4e0d\u5c11\u4eba\u5df2\u6210\u4e3a\u56fd\u9645\u4e0a\u7684\u8457\u540d\u5b66\u8005\uff0c\u8fd9\u4e00\u70b9\u5e7f\u4e3a\u4eba\u77e5\u3002\u4ed6\u8fd8\u70ed\u5fc3\u4e8e\u9ad8\u4e2d\u7684\u6570\u5b66\u6559\u80b2\uff0c\u81ea\u5df1\u4eb2\u81ea\u5199\u8bb2\u4e49\uff0c\u5bf9\u6570\u5b66\u6559\u80b2\u6240\u5e94\u6709\u7684\u59ff\u6001\u4f5c\u4e86\u6df1\u523b\u7684\u601d\u8003\u3002\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b60\u5c81\u5bff\u8fb0\u65f6\uff081963\uff09\uff0cP.S.Alexandrov\u548cB.V.Gnedenko\u4f5c\u4e86\u9898\u4e3a\u201c\u6559\u80b2\u5bb6\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u201d\u7684\u8bb2\u6f14\u3002\u4e0b\u9762\u53c2\u8003\u6b64\u6587\u8bb2\u8ff0\u4e00\u4e0b\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6570\u5b66\u6559\u80b2\u8bba\u3002\u82cf\u8054\u7684\u6559\u80b2\u5236\u5ea6\u4e0e\u65e5\u672c\u7a0d\u6709\u4e0d\u540c\uff0c\u4e3a\u5c0f\u5b66\uff087\uff5e10\u5c81\uff09\u3001\u521d\u4e2d\uff0811\uff5e14\u5c81\uff09\u3001\u9ad8\u4e2d\uff0815\uff5e17\u5c81\uff09\u3001\u5927\u5b66\uff0818\u5c81\uff5e20\u5c81\uff09\uff0c\u5728\u5927\u5b66\u91cc\u6570\u5b66\u4e13\u4e1a\u4e0e\u7269\u7406\u4e13\u4e1a\u5728\u4e00\u4e2a\u7cfb\uff08\u79f0\u4f5c\u6570\u5b66\u7269\u7406\u7cfb\uff09\u91cc\u3002\u9ad8\u4e2d\u76f8\u5f53\u4e8e\u65e5\u672c\u7684\u9ad8\u4e2d2\u5e74\u7ea7\u5230\u5927\u5b661\u5e74\u7ea7\uff0c\u5927\u5b66\u76f8\u5f53\u4e8e\u65e5\u672c\u7684\u5927\u5b662\u5e74\u7ea7\u81f3\u7855\u58eb\u7814\u7a76\u751f\u3002\u6709\u4e9b\u7c7b\u4f3c\u4e8e\u65e5\u672c\u7684\u65e7\u5236\u9ad8\u4e2d\u548c\u5927\u5b66\uff0c\u5927\u5b66\u6bd5\u4e1a\u65f6\u8981\u5199\u8bba\u6587\u83b7\u53d6\u5b66\u4f4d\uff0c\u76f8\u5f53\u4e8e\u65e5\u672c\u7684\u7855\u58eb\u5b66\u4f4d\u3002\u535a\u58eb\u5b66\u4f4d\u6388\u7ed9\u5927\u5b66\u6bd5\u4e1a\u540e\u5199\u8fc7\u8bb8\u591a\u521b\u4f5c\u8bba\u6587\u7684\u7279\u522b\u4f18\u79c0\u7684\u5b66\u8005\u3002<\/p>\n
\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u8ba4\u4e3a\uff0c\u6709\u4e9b\u5bb6\u957f\u548c\u6559\u5e08\u4f01\u56fe\u4ece10\u5c81\u523012\u5c81\u5de6\u53f3\u7684\u5b66\u751f\u4e2d\u6316\u6398\u6709\u6570\u5b66\u624d\u80fd\u7684\u5b69\u5b50\uff0c\u8fd9\u6837\u505a\u4f1a\u5bb3\u4e86\u5b69\u5b50\uff0c\u4f46\u662f\u5b69\u5b50\u5230\u4e8614\u81f316\u5c81\u65f6\uff0c\u60c5\u51b5\u5c31\u4e0d\u4e00\u6837\u4e86\u3002\u4ed6\u4eec\u5bf9\u6570\u5b66\u7269\u7406\u7684\u5174\u8da3\u5df2\u5f88\u6e05\u695a\u5730\u8868\u73b0\u4e86\u51fa\u6765\uff0c\u6839\u636e\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u5728\u9ad8\u4e2d\u6559\u6388\u6570\u5b66\u7269\u7406\u7684\u7ecf\u9a8c\uff0c\u5927\u7ea6\u6709\u4e00\u534a\u7684\u5b66\u751f\u8ba4\u4e3a\u6570\u5b66\u7269\u7406\u5bf9\u81ea\u5df1\u4ec5\u6709\u5f88\u5c0f\u7684\u4f5c\u7528\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u5b66\u751f\u5e94\u8be5\u5b89\u6392\u7b80\u5355\u5185\u5bb9\u7684\u8bfe\u7a0b\u3002\u8fd9\u6837\uff0c\u53e6\u4e00\u534a\u7684\u5b66\u751f\uff08\u5e76\u4e0d\u4e00\u5b9a\u4ed6\u4eec\u90fd\u8981\u641e\u6570\u5b66\u7269\u7406\u4e13\u4e1a\uff09\u7684\u6570\u5b66\u6559\u80b2\u5c31\u53ef\u4ee5\u66f4\u6709\u6548\u5730\u8fdb\u884c\u3002<\/p>\n
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\u6570\u5b66\u9700\u8981\u7279\u522b\u7684\u624d\u80fd\u8fd9\u4e00\u8bf4\u6cd5\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u662f\u8fc7\u4e8e\u5938\u5f20\u4e86\u3002\u6570\u5b66\u662f\u7279\u522b\u96be\u7684\u79d1\u76ee\u8fd9\u4e00\u5370\u8c61\u53ef\u80fd\u662f\u4ea7\u751f\u4e8e\u7b28\u62d9\u7684\u3001\u6781\u5176\u6559\u6761\u7684\u6559\u5b66\u65b9\u6cd5\u3002\u5982\u679c\u6709\u597d\u7684\u6559\u5e08\u548c\u597d\u7684\u6559\u79d1\u4e66\uff0c\u6b63\u5e38\u7684\u5e73\u5747\u7a0b\u5ea6\u7684\u4eba\u7684\u80fd\u529b\u8db3\u4ee5\u6d88\u5316\u9ad8\u4e2d\u6570\u5b66\uff0c\u5e76\u8fdb\u4e00\u6b65\u7406\u89e3\u5fae\u79ef\u5206\u7684\u521d\u6b65\u77e5\u8bc6\u3002<\/p>\n
\u7136\u800c\uff0c\u9ad8\u4e2d\u751f\u5728\u9009\u62e9\u6570\u5b66\u4f5c\u4e3a\u4e0a\u5927\u5b66\u7684\u4e13\u4e1a\u65f6\uff0c\u81ea\u7136\u5e94\u6d4b\u9a8c\u4e00\u4e0b\u81ea\u5df1\u5bf9\u6570\u5b66\u7684\u9002\u5e94\u6027\u3002\u5b9e\u9645\u4e0a\uff0c\u5728\u7406\u89e3\uff08\u6570\u5b66\u7684\uff09\u63a8\u8bba\u3001\u89e3\u51b3\u95ee\u9898\u3001\u6216\u4f5c\u51fa\u65b0\u7684\u53d1\u73b0\u4e0a\uff0c\u5176\u901f\u5ea6\u3001\u5bb9\u6613\u7a0b\u5ea6\u548c\u6210\u529f\u5ea6\u662f\u56e0\u4eba\u800c\u5f02\u7684\u3002\u5728\u6570\u5b66\u4e13\u4e1a\u6559\u80b2\u4e2d\uff0c\u5e94\u9009\u62e9\u5728\u6570\u5b66\u9886\u57df\u51fa\u6210\u5c31\u7684\u53ef\u80fd\u6027\u5927\u7684\u9752\u5e74\u4eba\u3002<\/p>\n
\u4ec0\u4e48\u662f\u5bf9\u4e8e\u6570\u5b66\u7684\u9002\u5e94\u6027\u5462\uff1f\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u603b\u7ed3\u4e3a\u4ee5\u4e0b\u4e09\u70b9\uff1a<\/p>\n
(1)\u7b97\u6cd5\u80fd\u529b\uff1a\u5373\u5bf9\u4e8e\u590d\u6742\u5f0f\u5b50\u4f5c\u9ad8\u660e\u7684\u53d8\u5f62\uff0c\u5bf9\u4e8e\u7528\u6807\u51c6\u65b9\u6cd5\u89e3\u4e0d\u4e86\u7684\u65b9\u7a0b\u5f0f\u4f5c\u5de7\u5999\u7684\u89e3\u51b3\u7684\u80fd\u529b\uff08\u4ec5\u8bb0\u4f4f\u8bb8\u591a\u5b9a\u7406\u3001\u516c\u5f0f\u662f\u4e0d\u884c\u7684\uff09\u3002<\/p>\n
(2)\u51e0\u4f55\u5b66\u76f4\u89c2\uff1a\u5bf9\u4e8e\u62bd\u8c61\u7684\u4e1c\u897f\uff0c\u80fd\u591f\u5728\u5934\u8111\u4e2d\u50cf\u753b\u753b\u4e00\u6837\u63cf\u7ed8\u51fa\u6765\u5e76\u52a0\u4ee5\u601d\u8003\u3002<\/p>\n
(3)\u4f5c\u903b\u8f91\u6027\u63a8\u7406\u7684\u80fd\u529b\uff1a\u4f8b\u5982\u80fd\u591f\u6b63\u786e\u5730\u5e94\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\u3002<\/p>\n
\u4ec5\u6709\u8fd9\u4e9b\u80fd\u529b\uff0c\u800c\u5bf9\u7814\u7a76\u9898\u76ee\u4e0d\u62b1\u6709\u5f3a\u70c8\u7684\u5174\u8da3\u3001\u4e0d\u4f5c\u6301\u4e45\u4e0d\u65ad\u7684\u7814\u7a76\u6d3b\u52a8\u7684\u8bdd\uff0c\u8fd8\u662f\u8d77\u4e0d\u4e86\u4ec0\u4e48\u4f5c\u7528\u3002<\/p>\n
\u5728\u5927\u5b66\u7684\u6570\u5b66\u6559\u80b2\u4e2d\uff0c\u597d\u7684\u6559\u5e08\u53c8\u662f\u4ec0\u4e48\u6837\u7684\u5462\uff1f<\/p>\n
(I)\u8bb2\u8bfe\u9ad8\u660e\u3002\u5982\u7528\u5176\u5b83\u7684\u79d1\u5b66\u9886\u57df\u7684\u4f8b\u5b50\u6765\u5438\u5f15\u5b66\u751f\u3002<\/p>\n
(II)\u4ee5\u6e05\u6670\u7684\u89e3\u91ca\u548c\u5bbd\u5e7f\u7684\u6570\u5b66\u77e5\u8bc6\u6765\u5438\u5f15\u5b66\u751f\u3002<\/p>\n
(III)\u5584\u4e8e\u4f5c\u4e2a\u522b\u6307\u5bfc\u3002\u6e05\u695a\u6bcf\u4e2a\u5b66\u751f\u7684\u80fd\u529b\uff0c\u5728\u5176\u80fd\u529b\u8303\u56f4\u5185\u5b89\u6392\u5b66\u4e60\u5185\u5bb9\uff0c\u4f7f\u5b66\u751f\u589e\u5f3a\u81ea\u4fe1\u5fc3\u3002<\/p>\n
\u4ee5\u4e0a\u6bcf\u4e00\u6761\u90fd\u662f\u6709\u4ef7\u503c\u7684\uff0c\u800c\u7406\u60f3\u7684\u6559\u5e08\u5e94\u5c5e(iii)\u7c7b\u578b\u7684\u6559\u5e08\u3002<\/p>\n
\u5bf9\u4e8e\u6570\u5b66\u7269\u7406\u7cfb\u7684\u5b66\u751f\u7684\u6570\u5b66\u6559\u80b2\uff0c\u9664\u4e86\u5e38\u89c4\u7684\u8bfe\u7a0b\uff0c\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7279\u522b\u5f3a\u8c03\u4e86\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n
(I)\u4f7f\u5b66\u751f\u80fd\u591f\u628a\u6cdb\u51fd\u5206\u6790\u4f5c\u4e3a\u65e5\u5e38\u5de5\u5177\u90a3\u6837\u8fd0\u7528\u81ea\u5982\u3002<\/p>\n
(II)\u91cd\u89c6\u5b9e\u9645\u95ee\u9898\u3002<\/p>\n
\u6211\u6700\u521d\u5bf9\u8fd9\u4e2a\u610f\u601d\u4e0d\u5927\u660e\u767d\uff0c\u6700\u8fd1\u89c1\u5230\u4e00\u4f4d\u66fe\u7ecf\u5728\u83ab\u65af\u79d1\u5927\u5b66\u63a5\u53d7\u8fc7\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u6307\u5bfc\u7684\u5148\u751f\uff0c\u4fbf\u8be2\u95ee\u4e86\u4e00\u4e0b\uff0c\u5176\u610f\u601d\u53ef\u80fd\u662f\u8fd9\u6837\u7684\uff0c\u4f8b\u5982\u5bf9\u4e8e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7ed9\u51fa\u5177\u4f53\u7684\u7cfb\u6570\u548c\u8fb9\u754c\u6761\u4ef6\uff08\u6bcf\u4e2a\u5b66\u751f\u4e0d\u540c\uff09\uff0c\u7136\u540e\u8ba9\u5b66\u751f\u8003\u5bdf\u65b9\u7a0b\u5f0f\u7684\u89e3\u7684\u6027\u8d28\u3002<\/p>\n
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From Jinshan: \u5f53\u5e74\u770b\u4e86\u300a\u6982\u7387\u8bba\u5bfc\u5f15\u300b\u4e4b\u540e\u5dee\u70b9\u53bb\u5b66\u6570\u5b66\u3002\u771f\u7684\u662f\u4f1f\u5927\u7684\u4eba\u548c\u4f1f\u5927\u7684\u4e66\u3002\u300a\u6982\u7387\u8bba\u5bfc\u5f15\u300b\u4e2d … \u7ee7\u7eed\u9605\u8bfb\u201c\u8f6c\u5e16\uff1a\u4f0a\u85e4\u6e05\u300aKolmogorov \u7684\u6578\u5b78\u89c0\u8207\u696d\u7e3e\u300b\u201d<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts\/1589"}],"collection":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/comments?post=1589"}],"version-history":[{"count":0,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts\/1589\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/media?parent=1589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/categories?post=1589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/tags?post=1589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}