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I have often been curious about the proofs in my Statistical Inference class, but often I have been told that it is not important to know all the details. I have looked into some of the proofs and found that Measure Theory plays a big role in probability. I will be taking Measure Theory soon.

What are some good books that go more in depth regarding these two topics?

pfmr1995
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  • Probability and measure by P. Billingsly and the book by K R Parthasarathy with the same title. – Kavi Rama Murthy Nov 18 '18 at 23:38
  • Probability and Measure Theory, by Robert B. Ash. A text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. – Alonso Delfín Nov 19 '18 at 02:09
  • What proofs are you interested in? Quite possibly, they are proofs that will not require measure theory. One might say that a basic course on probability is "in between" a course in statistics and a course in measure theory. Some good non-measure theory probability books are by Sheldon Ross or Leon-Garcia. – Michael Nov 19 '18 at 06:13

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