A user's guide to measure theoretic probabilityPollard, David
A user's guide to measure theoretic probability
by Pollard, David · first published 2002
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This text is not just a presentation of mathematical theory, but also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguements and understand what they mean.
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…intermediate text is: 6.) Grimmett, G. and Stirzaker, D. (2001). "Probability and Random Processes" Oxford. At a more advanced level, a very good text is the following: 7.) Pollard, D. (2001). "A User's Guide to Measure Theoretic Probability" Cambridge. The standard advanced textbook is Durrett, R. (2005). "Probability: Theory and Examples" Duxbury. Machine learning research also reposes on optimization theory. A good starting book…
on “Learning About Statistical Learning” ↗…the same topic simultaneously, anyway. - Two books on measure-theoretic probability theory that are more readable than many of the usual suspects are "Probability with Martingales" by Williams and "A User's Guide to Measure-Theoretic Probability" by Pollard. There is also a nice book called "Probability through Problems" that develops the theory through a series of exercises.
on “Ask HN: Learning advanced math” ↗