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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

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marked as duplicate by Martin, Start wearing purple, Henry T. Horton, Micah, Serkan May 17 '13 at 0:10

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Similar discussion here – Stahl May 16 '13 at 21:59
@Stahl did not see that at first! thank you very much, I have decided to leave this on open to see if there are any newer suggestions – DanZimm May 16 '13 at 22:02
(just so you know, it's still 2013) – Stahl May 16 '13 at 22:27
the question was originally asked in 2011 – DanZimm May 16 '13 at 22:51
Right, I'm only saying because you said it was "asked in 2013" in the edit of your question, and you linked to your own question :) (I fixed it up for you) – Stahl May 16 '13 at 23:01
up vote 4 down vote accepted

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.

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thank you! I really appreciate this! – DanZimm May 16 '13 at 22:07
@amWhy: excellent suggestion and OP's love when they can get at answers! +1 – Amzoti May 17 '13 at 1:02
Thanks, Amzoti! A trend towards making these sorts of posts CW today/ goes back and forth. – amWhy May 17 '13 at 1:03

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!

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I appreciate the advice! I will be looking into both books! – DanZimm May 16 '13 at 22:03

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

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Are the answers to exercises available somewhere? – Thomas Ahle May 28 '14 at 22:00

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.

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