{"id":20111,"date":"2022-08-23T14:38:53","date_gmt":"2022-08-23T06:38:53","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=20111"},"modified":"2024-11-15T15:05:41","modified_gmt":"2024-11-15T07:05:41","slug":"%e5%af%a6%e8%ae%8a%e5%87%bd%e6%95%b8%e8%ab%96%e4%b8%80-real-analysis-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e5%af%a6%e8%ae%8a%e5%87%bd%e6%95%b8%e8%ab%96%e4%b8%80-real-analysis-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","title":{"rendered":"\u5be6\u8b8a\u51fd\u6578\u8ad6(\u4e00) Real Analysis I | \u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20111\" class=\"elementor elementor-20111\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-13d70f5a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"13d70f5a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-373a1db9\" data-id=\"373a1db9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-2c3529c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c3529c0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-128cf510\" data-id=\"128cf510\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f3e8fc1 elementor-widget elementor-widget-penci-info-box\" data-id=\"2f3e8fc1\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_76623\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t<div class=\"penci-ibox-stit\">Real Analysis I<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u5be6\u8b8a\u51fd\u6578\u8ad6(\u4e00)<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-76f0aacd elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"76f0aacd\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-76f0aacd\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"76f0aacd\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" 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                                             <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/www.math.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u61c9\u7528\u6578\u5b78\u7cfb<\/a>\u00a0\u63d0\u4f9b\u3002\u00a0<\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">This is the course designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.<\/p><p>\u00a0<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\uff1a<\/span><span style=\"font-size: 16px;\">A. Friedman, Foundations of modern analysis, Dover, New York, 1982.<\/span><\/p><p><span style=\"color: #ff00ff;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/span><\/p><p>\u00a0<\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">\u6388\u8ab2\u8001\u5e2b<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a0\u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u5b78\u5206<\/th><td class=\"\u3002\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a03\u5b78\u5206<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5e74\u5ea6<\/th><td bgcolor=\"#EEEEEE\">\u00a099\u5b78\u5e74\u5ea6<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5c0d\u8c61<\/th><td>\u00a0\u78a9\u58eb\u73ed\u5b78\u751f<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u9810\u5099\u77e5\u8b58<\/th><td bgcolor=\"#EEEEEE\">\u00a0Advanced calculus and general mathematical maturity.<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u63d0\u4f9b<\/th><td><i><\/i>\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0\u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a>\u00a0 \u00a0 <a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/a><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-38\" class=\"tablepress tablepress-id-38\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class1 \u8ab2\u7a0b\u4ecb\u7d39<br \/>\n\u7b2c\u4e00\u7ae0 Measure theory<br \/>\nClass1 \u8ab2\u7a0b\u5c0e\u8ad6<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=20134\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class2<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23042\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class3<br \/>\nSec.1.2. Measure <br \/>\nSec.1.3. Outer Me<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23048\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class4<br \/>\nSec.1.4. Constructing outer measure<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23054\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class5<br \/>\nSec.1.5-1.6 Lebesgue measure<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23060\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class6<br \/>\nSec.1.7 Metric space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23066\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class7<br \/>\nSec.1.8-1.9 Construction of metric outer meas<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23072\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class8<br \/>\nSec.1.9 Construction of metric outer measure<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23078\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class9<br \/>\nsec.1.10 Signed measure<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23084\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class10<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23090\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Integration<br \/>\nClass11<br \/>\nSec. 2.2 Operations on measurable functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23102\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class12<br \/>\nSec 2.3. Egoroffs Thm.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23108\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class13<br \/>\nSec 2.3 Egoroffs Thm.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23114\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class14<br \/>\nSec 2.4 Convergence in measure<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23120\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class15<br \/>\nSec 2.5 Integrals of simple functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23126\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class16<br \/>\nSec. 2.6 Integrable functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23132\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class17<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23138\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class18<br \/>\nSec. 2.7 Properties of integral<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23144\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class19<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23150\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class20<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23156\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class21<br \/>\nSec.2.9 DCT<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23176\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class22<br \/>\nSec. 2.10 Applications of DCT<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23182\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class23<br \/>\nSec 2.11 (Proper) Riemann integral<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23188\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class24<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23200\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class25<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23206\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class26<br \/>\nSec. 2.13. Lebesgue decomposition<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23212\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class27<br \/>\nSec. 2.13. Lebesgue decomposition<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23218\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class28<br \/>\nSec. 2.14 Fundamental Thm of Calculus on<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23224\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class29<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23230\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class30<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23236\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class31<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23242\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class32<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23248\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class33<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23254\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-38 from cache --><\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">This is the course designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u55ae\u5143\u4e3b\u984c<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e00\u7ae0 Measure theory<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Abstract measure theory<br \/>Lebesgue measure<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u7ae0 Integration<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Convergence theorems <br \/>(Monotone Convergence theorem, Dominated Convergence theorem, Fatou lemma) <br \/>Fubini theorem <br \/>Tonelli theorem <br \/>Lpspace <br \/>Completeness <br \/>Compactness<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e09\u7ae0<\/span> Metric spaces<\/td><td style=\"padding: 5px;\"><span class=\"text\">Arzela-Ascoli theorem<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">A. Friedman, Foundations of modern analysis, Dover, New York, 1982.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u5e73\u6642\u6210\u7e3e<\/span><\/td><td style=\"padding: 5px;\">1\/3<\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u8003<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">1\/3<\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u8003<\/span><\/td><td style=\"padding: 5px;\">1\/3<\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span>\n<table border=\"1\" cellspacing=\"0\">\n<tbody>\n<tr class=\"stitle\">\n<td bgcolor=\"#FFF3DB\"><strong> \u55ae\u5143\u4e3b\u984c<\/strong><\/td>\n<td bgcolor=\"#FFF3DB\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"padding:5px;\"><span class=\"text\">\u7b2c\u4e00\u7ae0 Measure theory<\/span><\/td>\n<td style=\"padding:5px;\"><span class=\"text\">Abstract measure theory<br \/>\n  Lebesgue measure<\/span><\/td>\n<\/tr>\n<tr>\n<td bgcolor=\"#f2f2ec\"; style=\"padding:5px;\"><span class=\"text\">\u7b2c\u4e8c\u7ae0 Integration<\/span><\/td>\n<td bgcolor=\"#f2f2ec\"; style=\"padding:5px;\"><span class=\"text\">Convergence theorems <br \/>\n  (Monotone Convergence theorem, Dominated Convergence theorem, Fatou lemma) <br \/>\n  Fubini theorem <br \/>\n  Tonelli theorem <br \/>\n  Lpspace <br \/>\n  Completeness <br \/>\n  Compactness<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"padding:5px;\"><span class=\"text\">\u7b2c\u4e09\u7ae0<\/span> Metric spaces<\/td>\n<td style=\"padding:5px;\"><span class=\"text\">Arzela-Ascoli theorem<\/span><\/td>\n<\/tr>\n<\/tbody>\n<br><br \/>\n\n<\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-44bdbd33 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"44bdbd33\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 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