The Elements of Integration and Lebesgue Measure

by Robert G. Bartle

Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results―the convergence theorems.

Genres: Mathematics

192 pages, Paperback

First published January 23, 1995

Reviews

[Dan · Rating 2 out of 5]

This was my Real Analysis - Measure Theory text book.

It was very basic, very clear, and had lots of details.

I don't like Real Analysis, but this was a pretty good way to learn about Measure Theory.

[afloatingpoint · Rating 3 out of 5]

5/28/2015: So far: A very rigorous text! However, I would refer to other sources (lecture videos, notes, etc.) to grasp a better initial understanding on measure theory itself, and a rather reasonable comparison of Riemann vs. Lebesgue integrals.

Note: MITOpenCourseWare unfortunately doesn't have the lecture videos available, but mathematicalmonk on youtube gives an understandable introduction to measure theory in his Probability Primer's series.

12/8/2015: We went through THE WHOLE BOOK in our measure theory class. I will not comment on how the professor taught the class, but I would have been a lot more pleased if there were more examples and some sort of solution manual/hints for problems in this book. In general, I think having some sort of verification for one's solutions for any problem is essential to her learning process.

[Juan Manuel · Rating 5 out of 5]

A very good introduction to measure theory. I read the first part of the book on my own and I found it way clearer than other classic books such as Rudin's.

[FluffyMao · Rating 5 out of 5]

Excellent primer on Lebegue integration & theory. Short & sweet. Good exercises.