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Taking an innovative approach to both content and methods, this book explores the foundations, basic concepts, and fundamental results of probability theory. Geared toward those unfamiliar with probability theory, it offers a firm basis for the study of topics related to the probability of mathematical statistics and to information theory.

The effective construction of probability spaces receives particular attention. Author Alfred Rényi—former Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theory—considered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rényi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.

The effective construction of probability spaces receives particular attention. Author Alfred Rényi—former Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theory—considered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rényi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.

Reprint of the Holden-Day, Inc., San Francisco, 1970 edition.

Alfred Renyi: The Happy Mathematician

Alfred Renyi (1921–1970) was one of the giants of twentieth-century mathematics who, during his relatively short life, made major contributions to combinatorics, graph theory, number theory, and other fields.

Reviewing *Probability Theory* and *Foundations of Probability* simultaneously for the *Bulletin of the American Mathematical Society* in 1973, Alberto R. Galmarino wrote:

"Both books complement each other well and have, as said before, little overlap. They represent nearly opposite approaches to the question of how the theory should be presented to beginners. Rényi excels in both approaches. *Probability Theory* is an imposing textbook. *Foundations* is a masterpiece."

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**In the Author's Own Words:**"If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."

"Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?" — Alfred Rényi

Availability | Usually ships in 24 to 48 hours |

ISBN 10 | 0486462617 |

ISBN 13 | 9780486462615 |

Author/Editor | Alfred Renyi |

Format | Book |

Page Count | 384 |

Dimensions | 5 3/8 x 8 1/2 |

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