Measure, Integration & Real Analysis
Quick Informations
Where to buy it: Official Website
Author: Sheldon Axler
Release date: December 24, 2019
Language: English
Personal Progress: I currently read the first two chapters.
Description
The best way to understand this book is by viewing it as the perfect continuation of classical Real Analysis and Linear Algebra in finite dimension. The first half of the textbook is dedicated to the notion of measure and the new powerful theory of integration it induces. The second half of the textbook is dedicated to infinite dimension vector spaces. The transition between these two subjects is very natural. This book covers what courses on Measure Theory, Lebesgue Integration, and Functional Analysis would cover.
Review
[I didn't finish the book yet.] Even if I read two chapters only, I can say that this book is amazing. I already learned so much from it. The transition from Understanding Analysis (which I read right before) to this book was very smooth. The explanations are clear and the structure of the book is very natural. For the moment, I would highly recommend it.
Exercises
The exercises in this textbook are by far those that took me the most time to solve in comparaison to the other textbooks I read. When I used to read this book (I hope that I will finish it one day), I remember that it could take me days, or even more than a week to complete the exercises in one single section. Of course, this is not a bad thing. Each exercise really forces you to fully understand the content of the section. The exercises are really good, creative, and useful.
Prerequisites
The first half of the textbook is the natural continuation of classical Real Analysis. The perfect textbook to read for this would be Understanding Analysis by Stephen Abbott. The second half of the textbook is the natural condition of Linear Algebra in finite dimension. The best textbook to read for this is probably Linear Algebra Done Right by Sheldon Axler, the same author.
Further Readinds
I didn't finish the book yet so for the moment, I don't have any recommendations for further readings.