Please Recommend a Good Book on Measure Theory

[brian44]

All the books I want to read about probability and statistical estimation require some understanding of measure theory. What is a good introductory text on measure theory you would recommend (assuming no prior knowledge of measure theory at all)? I want to be able to teach myself from the book as well so it can't be too esoteric.

thanks for your help

[Landau]

Very suited for self study: Capinski et al (http://www.amazon.com/Measure-Integral-Probability-Marek-Capinski/dp/1852337818).
Consise intro: Bartle (http://www.amazon.com/Elements-Integration-Lebesgue-Measure/dp/0471042226/ref=sr_1_1?ie=UTF8&s=books&qid=1253626265&sr=1-1).

[n!kofeyn]

Books that I've come across, but don't have too much experience with are:
Lebesgue Integration (http://www.amazon.com/Lebesgue-Integration-Universitext-Soo-Chae/dp/0387943579/ref=sr_1_1?ie=UTF8&s=books&qid=1253640794&sr=8-1) by Soo B. Chae
Lebesgue Integration on Euclidean (http://www.amazon.com/Lebesgue-Integration-Euclidean-Bartlett-Mathematics/dp/0763717088/ref=sr_1_1?ie=UTF8&s=books&qid=1253640828&sr=8-1) Space by Frank Jones
A Radical Approach to Lebesgue's Theory of Integration (http://www.amazon.com/Lebesgues-Integration-Mathematical-Association-Textbooks/dp/0521711835/ref=sr_1_6?ie=UTF8&s=books&qid=1253640828&sr=8-6) by David Bressoud

In my opinion Lebesgue measure theory and integration is one of those subjects where there isn't a great textbook. If I remember correctly, all three of the above books define measure by a different method. You just sort of have to go with one. I recently learned from Real Analysis by Royden, but I do not recommend that text at all. Although, I second the recommendation of Bartle's book. It concentrates solely on measure and integration, but it is very expensive for such a small book.

[jbunniii]

This probability book develops all the measure theory you need as you go along:

Probability and Measure (http://www.amazon.com/Probability-Measure-3rd-Patrick-Billingsley/dp/0471007102) by Patrick Billingsley

You will want to know non-measure theoretic (discrete) probability before reading Billingsley. For this I like:

An Introduction to Probability Theory and Its Applications, Vol. 1 (http://www.amazon.com/Introduction-Probability-Theory-Applications-Vol/dp/0471257087/ref=sr_1_1?ie=UTF8&s=books&qid=1254273357&sr=1-1) by William Feller