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

@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
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
I am voting to close as a duplicate, since this was asked many times before and I don't quite see the point in collecting the same list of books an $n$-th time. If an earth-shattering new book on measure theory has appeared in the last two years, my apologies. — Martin, May 16 '13 at 23:26
You can find many of those threads in the "Linked" and "Related" questions in the right hand column on this page. — Martin, May 17 '13 at 03:00
@Martin accidentally double clicked the upvote, sorry I took it away D: — DanZimm, May 17 '13 at 03:04

score 7 · Accepted Answer · answered May 16 '13 at 22:04

7

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.

answered May 16 '13 at 22:04

amWhy

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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 01:02
Thanks, Amzoti! A trend towards making these sorts of posts CW today/lately...it goes back and forth. – amWhy May 17 '13 at 01:03

score 3 · Answer 2 · answered May 16 '13 at 21:58

3

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!

answered May 16 '13 at 21:58

mathmatters

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

score 2 · Answer 3 · answered May 16 '13 at 23:12

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

answered May 16 '13 at 23:12

Elias Costa

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

score 1 · Answer 4 · answered May 16 '13 at 23:10

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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.

answered May 16 '13 at 23:10

Brian Rushton

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Book Suggestions for an Introduction to Measure Theory

4 Answers4

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