PROBABILITY AND MEASURE, 3RD EDITION (WILEY SERIES IN PROBABILITY AND MATHEMATICAL STATISTICS) by PATRICK BILLINGSLEY (PDF)

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*** International Edition ***

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The most detailed book on the subject. Easy to understand and you only need a little bit real analysis background before reading it. It also has many examples.

⭐Excellent for those interested in probability and statistics. Even with more modern books out (i.e. Durrett), I still consult this one the most. Make sure to find the 3rd edition, and not the anniversary edition.

⭐Just as a heads-up, this is the version from Wiley India, so it comes on recycled paper and does not look quite as fancy as you might be used to from US versions of math books.

⭐This book is a disaster to learn from. It is an extremely poorly organized book with nological structuring of the material. I do not believe that this is a good book to learnprobability and measure theory from. If you are not already familiar with most of the conceptsthen I recommend starting your journey elsewhere.

⭐Don’t buy the third edition (lots of typos and it’s more expensive), this is the good one.

⭐Its a very serious text of probability and measure.The exercises are interesting.

⭐THE REFERENCE for all others.

⭐This book was my first introduction into probability so I am somewhat sentimentally attached to it. The exposition is very, very careful and there is very little a reader has to do than to read carefully meaning that this text is a solid introduction to a serious probability for upper class undergraduates or beginning graduate students.As a graduate student I very much appreciated the rigor and detailed approach in this textbook. Some of the topics like independence and martingales are developed with a rigor and details usually missing from undergraduate textbooks. If you do not like books missing any deductions this is your textbook.But there are problems with the text, the major one being the outline and order of the exposition, sometimes it looks as if it was done at random though even that has been done with intention to facilitate understanding but has somehow gone a bit astray. For example it takes hundreds of pages to get into fairly elementary notions and then they are treated counterintuitive leaving reader without intuitive understanding of the topics. See for example exposition of expectation (general case) that is way too slow after hundreds of pages. Or discrete Markov Chains treatment early enough but completely technical and counterintuitive without ever leading a student to any concrete ideas. The integration topics are sprinkled all over the place as well.Still I would think this is the text for introductory study of probability only with a instructor furnishing better choice and order of topics than the one presented in the textbook. It surely is one of the most detailed approaches geared toward a serious study. On the level of sofistication it does not come anywhere close to Kallenberg’s “Foundations of Modern Probability” or Borovkov’s “Probability Theory” but it does provide a treatise with important examples, without omissions (sometimes on the expense of elegance but every time for the benefit of reader), and with a rigor required while still being accessible to a beginning graduate student and thus it provides the important benefits of learning.This is one of the plausible choices for two semester course in introductory graduate probability with perhaps Kai Lai Chung’s classic Stanford textbook as the alternative.

⭐I got this book as a pre lecture for my PhD-Project in probabilistic combinatorics, because my knowledge about measures (and its their use in probability) was bad. Other books I read had a focus either on just formal measure theory or probability theory like combinatorics. This book is really really good to read and you can gain a good understanding of probability, somewhere in between the necessary formalism and the intuition of a gambler’s game or throwing a coin.I would rather not recommend this book for entry level courses (like first semester of bachelor), because it is necessary to know the basics of analysis in R^n.The best exposition of probability from a master. Except the notation which is a bit old-fashioned this is still one of the best for advanced students in probability.

⭐Il libro in sé è molto interessante. Purtroppo è arrivato rovinato, ma avendone bisogno me lo sono tenuto così com’èquesto libro è la terza edizione di un famoso trattato. Devo dire che preferivo la seconda edizione, più estesa; ho dovuto fotocopiare le parti che l’autore ha eliminato dalla edizione attualeEl libro de Billingsley es un excelente libro de probabilidad rigurosamente fundamentado. Se responden a todas las cuestiones que surgen de manera natural en un lector con sensibilidad matemática. Trata también tópicos como los espacios Lp, diferentes tipos de convergencia, y procesos estocásticos. Además tiene una buena colección de ejercicios.

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