課程大綱及進度表
開課系所
數學系開課學年
101開課學期
1課程名稱(中文)
實變數函數論課程名稱(英文)
Real Analysis課程碼
C136200分班碼
先修科目或先備能力
學分數
3開課教師
吳順益電話
(06)2757575 轉 65133Office Hours
By Appointment課程概述
主要討論 Lebesque Measure、Lebesque Measurable Function 及 Lebesque Integration,主要是教導實變函數的基 礎概念。教學目標
主要是讓選這門課程的學生對 Lebesque Measure,與 Lebesque Integration 有 一些基礎概念。授課課程大綱明細
Chapter 1. Lebesgue measure1.1 Introduction
1.2 Lebesgue other measure
1.3 The ‐ Algebra of Lebesque Measure Sets
1.4 Outer and Inner Approximation of Lebesque
Measurable Sets
1.5 Countable Additivity, Continuity, and
the
Borel‐Contelli Lemma
Chapter 2. Lebesque Measurable Functions
2.1 Sums, Products, and Compositions 2.2 Sequential Pointwise Limits and Simple Approximation 2.3 Littlewood’s Three Principles, Egoroff’s
Theorem, and Lusin’s Theorem Chapter3. Lebesque Integration 3.1 The Riemann Integral
3.2 The Lebesuqe Integral of a Bounded Measurable Nonnegative Function over a set of
Finite Measure
3.3 The Lebesque Integral of a Measurable Nonnegative Function
3.4 The General Lebesque Integral 3.5 Countable Additivity and Continuity of Integration
3.6 Uniform Integrability: The Vitali Convergence
Theorem
Chapter4. Lebesque Integration:
Further Topics
4.1 Uniform Integrability and Tightness: A General Vitali Convergence Theorem 4.2 Convergence in Measure
4.3 Characterizations of Riemann and Lebesque
Integrability
參考書目 Real Analysis (Fourth Edition) by Halsey Royden and Patrick
Fitzpatrick
課程要求
評量方式
期中考:40%期末考:40%
平時成績:20%