Probability and Measure
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 probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory. Like the previous editions, this new edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory. --back cover
Stats for nerds
3recommend
5mentions
5people
2010–2025years
60% recommend20% neutral20% critical
Mentions per year
What Hacker News says
- William 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 Ito calculus/stochastics those 2 books are pretty good.
These books have some overlap between themselves but are pretty complementary overall. I would say Feller Volume 1 up to Chapter 11 is decent for non-math people, beyond that you need to be serious about learning.
Didn't put any statistics books as that's a whole different topic.
- 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 Theory
- 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.
- Pat Billingsley's Probability and Measure 3e. was reissued in an Anniversary Edition, which is just the same content but with several typographical errors.
- > 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" etc.
> You seem to be accepting of a conditional expectation.
Conditional expectation is defined in terms of conditional probabilities, and those are in turn explicitly defined as P(A|B)=P(A,B)/P(B), so there's nothing not to accept.
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