实变函数

学分：3学分

先修课程：实分析与微积分；向量、几何与线性代数；多元微积分与向量分析

课程描述及目标：

本课程提供了勒贝格可积理论和分析中基本技术的一个坚实基础。主要内容包括集合的m-代数，测度论，勒贝格可积理论，收敛定理，LP-空间和微分。希望修学本课程的学生应当有高等微积分和基本分析的知识。

修读完该课程后，学生应该懂得测度论的基本理论。

成绩评定方式：

评定：学期总评成绩（100％）

重评：补考卷面成绩（100％）

成绩评定要求出勤率

参考教材：

周性伟　编著，实变函数，科学出版社，2007.01，讲义随堂提供。

Real Analysis

Credits: 3 Credits

Pre-requisite: Real Analysis & the Calculus; Multivariable & Vector Analysis

Description：

This course provides a solid foundation in the Lebesgue integration theory and basic techniques in analysis. Topics include m-algebra of sets, measure theory, Lebesgue integration theory, convergence theorems, Lp-spaces and differentiation. Students taking this course are expected to have knowledge in advanced calculus and elementary analysis.

After this course, the students should understand the basic theory about the measure theory.

Methods of Summative Assessment：

Assessment: Assessments done during semester (100%)

Reassessment: best of 3 hour resit examination (100%)

Attendance at tutorials is a required element of this module.

Recommended textbooks：

Zhou Xingwei, Real Analysis, Science Press, 2007.01.

Detailed lecture notes will be provided to students