MATH 5140-0

Brief

This course is an introduction to the theory of measure and integration. In the first semester we will introduce Lebesgue’s theory of measure and integration. Topics to be covered include: 1. Preliminaries on set theory 2. Lebesgue measure 3. Lebesgue integral 4. Differentiation and integration In the second semester we will introduce abstract theory of measure and integration, and some elements of harmonic analysis.

Description

Course keywords: 可測集,measurable set,可測函數,measurable function,測度,measure,積分,integration,微分,differentiation,Lp空間,Lp space 一、課程說明(Course Description) This course is an introduction to the theory of measure and integration. In the second semester we will introduce some elements of functional analysis, abstract measure and integration. Topics to be covered include: 1. Introduction to Banach spaces and Lp 2. Introduction to Hilbert spaces and L2 3. Abstract measure and integration 4. Hausdorff measure and fractals 二、指定用書(Text Books) E. M. Stein and R. Shakarchi: Real Analysis, Princeton University Press, 2005. 三、參考書籍(References) 1. H. L. Royden: Real Analysis, Macmillian, 1988. 2. R. L. Wheeden and A. Zygmund: Measure and Integral - An introduction to Real Analysis, Marcel Dekker, 1977. 四、教學方式(Teaching Method) Traditional 五、教學進度(Syllabus) Chapters 4,6,7 of the textbook, plus some supplementary materials. 六、成績考核(Evaluation) Homework/Quizzes (20%): Selected exercises from Stein-Shakarchi’s book and supplementary materials will be assigned. Some of them will be collected and graded. Quizzes will be based on homework assignments. Further details will be available during the first week of classes. Two exams (80%): Each exam worth 40% of the course grade. 七、可連結之網頁位址 http://www.math.nthu.edu.tw/~kchen/teaching/5131S23.html

Timetable

Scores

Average GPA 2.77

Std. Deviation 1.13

Remarks

本課程上150分鐘，其餘時間由教授彈性運用。

Restrictions

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization