高等实分析
授课教师：沈舜麟
课程主页：2024Fall-AdvRA
Chapter 1: 测度论初步
- 半环-半代数-代数-σ代数
- 预测度-外测度-测度-测度完备化
- 重要定理：单调类定理，Carathéodory定理，Carathéodory延拓定理
- 课程文件：第二周概要 、第三周概要
- 课程作业解答：第一次习题课
Chapter 2: [积分论]
Chapter 3: [符号测度以及微分]
Chapter 4: [L^p空间]
Chapter 5: [Radon测度]
Chapter 6: [Fourier分析基础]
Chapter 7: [分布理论]
参考书目：
【1】Folland, G. B. (2013). Real analysis: modern techniques and their applications. John Wiley & Sons.
【2】严加安，测度论讲义 (2004).
【3】Rudin, W. (1987). Real and complex analysis. Tata McGraw-Hill Education.
【4】Stein, E. M., & Shakarchi, R. (2010). Real analysis: measure theory, integration, and Hilbert spaces. Princeton University Press.
- Title: 高等实分析
- Author: Gypsophila
- Created at : 2024-09-16 13:21:13
- Updated at : 2024-10-20 14:24:08
- Link: https://chenx.space/2024/09/16/AdvRealAnalysis/
- License: This work is licensed under CC BY-NC-SA 4.0.
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