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: https://www.amazon.com/dp/1852337818/?tag=pfamazon01-20.
Consise intro: https://www.amazon.com/dp/0471042226/?tag=pfamazon01-20.

 

[n!kofeyn]

Books that I've come across, but don't have too much experience with are:
https://www.amazon.com/dp/0387943579/?tag=pfamazon01-20 by Soo B. Chae
https://www.amazon.com/dp/0763717088/?tag=pfamazon01-20 Space by Frank Jones
https://www.amazon.com/dp/0521711835/?tag=pfamazon01-20 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:

https://www.amazon.com/dp/0471007102/?tag=pfamazon01-20 by Patrick Billingsley

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

https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20 by William Feller