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Probability Theory

Alfréd Rényi
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Mihaela Poplicher
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This Dover edition is an unabridged republication of the work published in 1970 by North-Holland Publishing Company, Amsterdam, and Akadémiai Kiadó, the Publishing House of the Hungarian Academy of Sciences, Budapest. It is the last work of the famous Hungarian mathematician Alfréd Rényi, who taught at the University of Budapest and many other universities, and was the director of the Mathematical Institute of the Hungarian Academy of Sciences.

Rényi is considered to be the founder of Hungary’s Probability Theory School, though he also made several significant contributions to other areas of mathematics. He died suddenly in 1970, before he could proof-read the final version of this book. His memory is very well-respected in Hungary to this day.

This is an introductory text in probability theory and requires no prior knowledge of the subject. It is based on the author’s teaching experience at the University of Budapest, and on the lecture notes he prepared for his lectures beginning in 1954. The reader is expected to posses a good understanding of differential and integral calculus, as well as real and complex functions.

With chapters such as Algebras of Events, Probability, Random Variables (3 chapters), Characteristic Functions, Laws of Large Numbers, and The Limit Theorems of Probability Theory, the book covers the standard topics of an introduction to probability theory. The treatment of the subject is self-contained, rigorous and challenging.

For the interested student in particular, the exercises included at the end of each chapter should be extremely helpful. For the probability theorist, the book offers a somewhat different prospective, as well as a useful Appendix: Introduction to Information Theory.

Despite the fact that it was written so many years ago, this beautifully written book has much to offer to readers today, including many ideas for introductory courses in probability theory at the undergraduate or graduate level.

Mihaela Poplicher is an associate professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is

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