https://rubatotree.github.io/blog/tags/%E5%88%86%E6%9E%90/Recent content in 分析 on Umbrella Coffeehttps://rubatotree.github.io/blog/images/og-default.pnghttps://rubatotree.github.io/blog/images/og-default.pngHugoen-usTue, 10 Jun 2025 00:00:00 +0800https://rubatotree.github.io/blog/posts/ra-note/Tue, 10 Jun 2025 00:00:00 +0800https://rubatotree.github.io/blog/posts/ra-note/<p>这是我在 2025 年春季于中科大学习<a href="https://faculty.ustc.edu.cn/yushucheng/zh_CN/index.htm" target="_blank" rel="noopener noreferrer"><span style="color: #59a4ff;"><span style="text-decoration: underline">于树澄</span></span></a>老师的《实分析》<a id="loc-1" href="#loc-48" role="doc-biblioref">[1]</a> 课程时整理的期末考试复习笔记。课程录像已有同学上传到 <a href="https://www.bilibili.com/video/BV1LRJHz9Eub" target="_blank" rel="noopener noreferrer"><span style="color: #59a4ff;"><span style="text-decoration: underline">Bilibili</span></span></a>.</p> <h2 id="loc-2">实分析复习笔记 期中部分</h2> <h3 id="loc-3">Lebesgue 测度的建立</h3> <h4 id="loc-4">1. 集合论基础：规定一类集合的代数性质，使得简单生成元上的性质可被推广</h4> <p></p> <ol> <li value="1">集合的运算，集合列的极限，点集拓扑</li> </ol> <p></p> <p></p> <ul> <li> <p><strong>作业 1a.3</strong>：上下极限的等价表述</p> <p></p> <ul> <li><span role="math"><svg class="typst-frame" style="overflow: visible; width: 3.0949999999999998em; height: 0.683em;" viewBox="0 0 41.7825 9.2205" width="41.7825pt" height="9.2205pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:h5="http://www.w3.org/1999/xhtml"><g><g class="typst-text" transform="matrix(1 0 0 -1 0 9.2205)"><use xlink:href="#g7FA5977BD6AF286C6FF8EDE62B3E9C33" x="0" y="0" fill="#000000" fill-rule="nonzero"/><use xlink:href="#gEFB0D4954C8ADA240A829471597EA46F" x="3.753" y="0" fill="#000000" fill-rule="nonzero"/><use xlink:href="#g50DA4B7BDD6A87E9D1327A0524772811" x="7.506" y="0" fill="#000000" fill-rule="nonzero"/><use xlink:href="#gF1E3D149091ABEF4B289FED13C61F321" x="21.4515" y="0" fill="#000000" fill-rule="nonzero"/><use 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