{"id":845,"date":"2021-05-23T18:22:03","date_gmt":"2021-05-23T10:22:03","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=845"},"modified":"2022-10-12T17:17:26","modified_gmt":"2022-10-12T09:17:26","slug":"lebesgue_cover_theorem","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2021\/05\/23\/lebesgue_cover_theorem\/","title":{"rendered":"Lebesgue\u8986\u76d6\u5b9a\u7406\u8bc1\u660e\u7ec6\u8282\u6ce8\u89e3"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u8bc1\u660e\u8be6\u89c1\u4e66\u4e0aP115-P116, \u6709\u7591\u95ee\u7684\u70b9\u5728\u4e8eP116\u7b2c\u4e8c\u6bb5: \u53ef\u4ee5\u53d6\u4e00\u4e2a$k_u \\in \\mathbb{N}$, \u4f7f\u5f97$\\{U \\in 2^{-k_i} \\mathcal{W} \\ | \\ U \\cap \\bar{A_i} \\ne \\emptyset\\}$\u6784\u6210\u8fd9\u4e2a\u8986\u76d6\u7684\u5f00\u52a0\u7ec6.<br \/>\n$\\\\$ \u6211\u4e2a\u4eba\u7684\u7406\u89e3\u662f: \u8ba8\u8bba\u7684\u5f00\u8986\u76d6$\\mathcal{U}$\u662f\u786e\u5b9a\u4e86\u7684, \u7531\u4e8e\u662f\u5728\u5ea6\u91cf\u7a7a\u95f4\u4e2d, \u90a3\u4e48\u5f00\u96c6\u65cf$\\mathcal{U}$\u603b\u6709\u4e00\u4e2a&#8221;\u534a\u5f84&#8221;\u6700\u5c0f\u7684\u5f00\u96c6(\u4e0d\u59a8\u8bbe\u4e3a$M$), \u56e0\u6b64\u603b\u53ef\u4ee5\u53d6\u4e00\u4e2a$k_u \\in \\mathbb{N}$\u4f7f\u5f97$\\{U $$ \\in 2^{-k_i}\\mathcal{W}|U \\cap \\bar{A_i} \\ne \\emptyset\\}$\u4e2d\u7684\u5143\u7d20\u7684\u534a\u5f84\u662f\u6bd4$M$\u7684\u534a\u5f84\u8fd8\u5c0f\u7684, \u90a3\u4e48\u7531\u5f00\u52a0\u7ec6\u7684\u5b9a\u4e49\u53ef\u77e5\u8fd9\u6837\u7684\u53d6\u6cd5\u662f\u53ef\u884c\u7684.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8bc1\u660e\u8be6\u89c1\u4e66\u4e0aP115-P116, \u6709\u7591\u95ee\u7684\u70b9\u5728\u4e8eP116\u7b2c\u4e8c\u6bb5: \u53ef\u4ee5\u53d6\u4e00\u4e2a$k_u \\in \\mathbb{ &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2021\/05\/23\/lebesgue_cover_theorem\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">Lebesgue\u8986\u76d6\u5b9a\u7406\u8bc1\u660e\u7ec6\u8282\u6ce8\u89e3<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/845"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=845"}],"version-history":[{"count":12,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/845\/revisions"}],"predecessor-version":[{"id":2470,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/845\/revisions\/2470"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=845"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}