Study Materials of the Math Textbook

Folland, G. B. (2013). Real Analysis: Modern Techniques and their Applications. John Wiley & Sons.

I wrote and provide the following PDF materials on some of the statements and chapters in the textbook. This might help understand theorems/statements/exercises shown in the textbook and the backgrounds behind them.

- Chapter 1.1 (Measures) Introduction

Necessity of Restricting the Domain of a Volume Function (a.k.a. Lebesque Measure). [ PDF ]

- Chapters 1.2, 2.1, 2.4 -Algebra and Measurable Functions

Abstract -Algebra and Measurable Functions (with Some Topology and Set Theory). [ PDF ]

- Chapter 1.3 (Measures) Measures

Proofs of Some Statements and Exercises in Chapter 1.3. [ PDF ]

- Chapters 3.1, 3.2 (Signed Measures & Differentiation) Signed Measures and the Lebesque-Radon-Nikodym Theorem

The (Lebesque-)Radon-Nikodym Theorem and Jordan Decomposition. [ PDF ]