Real Analysis

Introduction

Real analysis is the basis of advanced analysis theory, and is also an important tool commonly used in other fields, such as harmonic analysis, partial differential equations, probability theory and so on.

Assignment

2018-1

• Chapter 1: Preliminaries
  
• Chapter 2: Functions of Bounded Variation and the Riemann–Stieltjes Integral
  
• Chapter 3: Lebesgue Measure and Outer Measure
  Hw1,   Hw2
• Chapter 4: Lebesgue Measurable Functions
  Hw3,   Hw4
• Chapter 5: The Lebesgue Integral
  Hw5,   Hw6
• Chapter 6: Repeated Integration
  Hw7,   Hw8
• Chapter 7: Differentiation
  Hw9,   Hw10
  
  

2018-2

• Chapter 8: \(L^p\) Classes
  Hw1
• Chapter 9: Approximations of the Identity and Maximal Functions
  Hw2
• Chapter 10: Abstract Integration
  Hw3,   Hw4,   Hw5,   Hw6
  
• Chapter 11: Outer Measure and Measure
  Hw7,   Hw8,   Hw9
• Supplement: Introduction to the theory of distributions (Chapter 1 - 2)
  Hw10
  
  

2019-1

• Chapter 1: Measure Theory
  Hw1,   Hw2,   Hw3,   Hw4
  
• Chapter 2: Integration Theory
  Extra Hw,   Hw5
  
• Chapter 3: Construction of Measures
  Hw6
  
• Chapter 4: Product Measures
  Hw7
  
  

Text Book

1. (2018) Measure and Integral: An Introduction to Real Analysis
   Richard L. Wheeden and Antoni Zygmund, Second Edition
   
   
   
   
   
2. (2018-2) Introduction to the theory of distributions
   F. G. Friedlander and M. Joshi, Second Edition
   
   
   
   
   
3. (2019-1) Real Analysis
   Elias M. Stein and Rami Shakarchi