First Look At Rigorous Probability Theory, A (2Nd Edition)

I bought this book because it was good value. Having worked through it I have to say that Rosenthal is a lot smarter than I am and I had to look at other sources to fill in some of the gaps in his proofs. The book covers a lot in 200 pages and this is at the expense of detail. One thing that frustrated me was the exercises with no solutions. This is a good book but you are going to need some additional sources to work out wtf is going on at times.

This was the first book I bought when I was learning advanced probability theory. I've also used Billingsley (a classic, but a little hard to digest) & Ash & Doleans-Dade (very well written and a comprehensive text), but often return to Rosenthal because the fundamentals are so clearly explained and the language and organization of the book make such sense. The book is fairly short, yet covers the important topics very well. Proofs are sometimes not as rigorously developed as some might prefer, but I found them sufficient for an introductory text. Exercises are reasonable, but I would have traded a few more remarks, examples, and narrative for some of them. Generally, an outstanding introductory text.

I don't know if first look is the right title. I learned a lot working through this book by myself, but progress was pretty slow sometimes. There is a lot of work you need to do on your own to fill out missing parts of the proofs. If you've never seen this stuff before, I think it would be pretty difficult to work everything out on your own. Otherwise I thought the book was very strong, and covered a lot of useful material.

Good price

I bought this book expect to receive a brilliant triumph of clear insightful explanation about probability with measure theory. The first thing I noticed when I open the book is that the print is small. I also noticed that every page was covered with equations and the equations were often bunched up in messy bunches. This made me curious about how many figures were in this brilliantly insightful book. There are 5 figures in this book. I am beginning to think that this is a standard formal presentation of probability with measure theory. Here is a quote from the appendix which is referred to in the first few pages. "A set is countable if for some function f : N -> omega, we have f(N) = omega. (Note that, by this definition, all finite sets are countable. As a special case, the empty set phi is both finite and countable). A set is countably infinite if it is countable but not finite." I took the liberty of writing out the Greek letters in English. I know about countably infinite, but I don't think he is struggle hard to be clear here.

This is a great book for learning mathematically rigorous probability theory. Concepts are motivated and presented as needed.

Ok textbook but useful reference for any graduate math or stat person.

Excellent one! Well explained. If you want to teach or want to learn probability this book is definitely recommended.

I used this book to review some measure theory, and to focus it into probability. It does the world a service in at least two ways: (a) making the connection between measure theory and probability which isn't as intuitive as one may think, and (b) describing concepts in a succinct manner.It is also useful as a reference. Due to its brevity, you can find exactly what you need in seconds. It reads like cherished notes, but also does not dispense with rigour; it's full of proofs. He elucidates heuristic patterns, like the formulation of integrals from simple functions up to integrable ones.I recommend this text highly.

I wish to congratulate the author on writing such a great book. There aren't very many books that cover the topic of probability theory so well and are *readable* at the same time. I cannot recommend this book enough.

Summary: Short, lucid and terse introduction to measure theoretic probability for those with a some background in mathematicsBackground and Comparison: I came to this book after Rohatgi. Rohatgi had some excellent exercises, but it followed a statistical path that I didn't want to follow it on. Further, Rohatgi (as most probability books) took some things for granted, for example, some of the definitions in the probability space like sigma algebras.About this book:This book formally introduces probability and does it really well. It's short - just around 170 pages, but the exercises are well written and the rigor is excellent. While maintaining rigour, it doesn't lose lucidity. Thus it falls into a small class of mathematical books like baby Rudin and Axler that use notations to their advantage than as a barrier to fresh students.Recommendation:This is recommended as a third (level) probability book (or as a companion book to L2) where:L1: Sheldon Ross - First Course in probability, FellerL2: Rohatgi, Sheldon Ross - Probability Models, Grimmett-StirzakerL3: Rosenthal, Billingsley, Williams (Probability with Martingales), ParthasarathySuitable for Course?Not by itself, unless the course is on measure theoretic probability. It should be used as a companion book. It would be difficult as self study material unless reader has been introduced to the material elsewhere.Exercises:Very doable. Thus is not a monograph. It contain exercises for one to work through to ensure one understands the material.

Gentle introduction to measure theoretic probability.Pros* Easy to read and understand* Minimal prerequisitesCons* Does not use the most general framework to prove theorems* Difficult to find theorems to reference* Ordering and grouping of material is not very logical, for example the convergence theorems are not grouped together

Clear and rigorous, an exceptional book that introduces the probability theory, the language is very simple and nothing is left to the reader. Absolutely to be read