Probability and Measure
by Patrick Billingsley · first published 1979
60% recommend20% neutral20% critical
Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional
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If you already know analysis (well), the best probability book is "Probability & Measure" by Billingsley. A gentler introduction is the SUMS book "Measure, Probability, and Integral." If you don't care about measure theory and just want to learn how to calculate the probability that a coin comes up heads in the first five attempts, the book by Larsen and Marx is pretty good.
on “Ask HN: Learning advanced math” ↗Always within arm's reach at both home and work: Rudin, Real and Complex Analysis Halmos, Finite Dimensional Vector Spaces Billingsley, Probability and Measure Kelley, General Topology Lang, Undergraduate Algebra Simmons, Introduction to Topology and Modern Analysis Parthasarathy, Probability Measures on Metric Spaces Whinston, Green and Mas-Colell, Microeconomic…
on “Ask HN: What books do you keep on your desk?” ↗…Feller: An introduction to Probability Theory and Its Applications Volumes 1 and 2 - Volume 1 is considered the "classic" in most math undergrad courses, Volume 2 is for masters level students. Billingsley Probability and Measure - For more advanced probability you need to know measure theory, this is a book dedicated to that. Karlin + Taylor - First (and Second) Course in Stochastic Processes - If you are interested in learning…
on “Ask HN: List of best probability books from beginner to advance?” ↗> I think picking up a standard graduate probability book will clear this up better than any long comment trail. Can you recommend one? I just picked up Probability and Measure by Billingsley and it does not mention "conditional random variable" a single time in over 600 pages. It does have a lot of "conditional probability", "conditional distribution", "conditional expectation"…
on “Derive Yourself a Kalman Filter” ↗Pat Billingsley's Probability and Measure 3e. was reissued in an Anniversary Edition, which is just the same content but with several typographical errors.
on “Older editions of which books were better than the new ones? (2010)” ↗