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I'm looking for good lecture notes (or concise books) that develop probability theory from a measure theoretic point of view. In particular, I'm looking for a text where the measure theoretic part is developed only as far as needed for probability theory. (I'm not really interested in measure theory on its own.)

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Does any one know anything about the book by Krishna Athreya, Measure Theory and Probability Theory? I ask because I know it is available on Springer Link as a PDF, which is free if your university has a subscription. So, it's an actual textbook, but with the same cost as lecture notes. – Graphth Aug 27 '12 at 17:01
I wonder how is it possible to distinguish a part of measure theory which is not needed for probability. – Ilya Aug 27 '12 at 20:19
up vote 7 down vote accepted

My favorite introduction to measure theoretic probability is Probability with Martingales by David Williams. The book is very well written and fun to read.

A text that is easier, but IMO less fun is A Probability Path by Sidney Resnick. That book provides you with all the details and does everything in small steps.

A very concise book that contains the essentials is Probability Theory by S. R. S. Varadhan

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I suggest A first look at rigorous probability by Jeffrey Rosenthal.

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I second this response – Logarithm May 6 '14 at 6:11

Although it is a rather thick book I recommend Billingsley's Probability and Measure.

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Although it is little terse, I like Durrett's Probability: Theory and Examples.

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I suggest David Pollard's A User's Guide to Measure Theoretic Probability, published in 2002.

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@did Thanks for putting in the link to the book on googlebooks – Dilip Sarwate Aug 27 '12 at 20:06
You are welcome. – Did Aug 27 '12 at 20:11

I'd recommend Doob's Measure Theory. It does a nice job at blending probability with measure theory, perhaps close to the style you're looking for.

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How about for a nice introduction...

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