Book Suggestions for an Introduction to Measure Theory

Question

Couldn't find this question asked anywhere on the site, so here it is! Do you guys have any recommendations for someone being introduced to measure theory and lebesgue integrals?

A mentor has suggested a book that's in french, but unfortunately I don't know french (heck I barely know english) - so english books only please!

Thanks in advanced!

EDIT: Did not realize this had been asked here but I'm going to leave this question open to see if there are any newer books (that question was originally asked in 2011). If I am doing something wrong here, just give me a gentle shoutout in the comments and I'll be understanding and close this

Answer 1

You might want to take a look at Schillings Measures, Integrals, and Martingales.

It's a great introductory text for Measure Theory, gentle, but rigorous. The author's website has solutions to the book, as well as Errata, etc. You can take a look at the table of contents in the link given above.

Answer 2

I would say Fremlin: Measure theory is a good choice (i guess it's freely available on the web). The best measure theory book i know is unfortunately in German (Elstrodt: Maß- und Integrationstheorie)

Hope your happy with Fremlin!

Answer 3

Frank Jone's Lebesgue Measure on Euclidean space is the greatest math book that I have ever read. It gives a very slow introduction to lebesgue measure. It is fabulous; I did every homework problem for fun.

Answer 4

I recomend An introduction to measure theory by Terence Tao ( Fields Medalist in 2006).