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 Rényiformer Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theoryconsidered 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.
About the Author
Alfred Renyi was Director of the Mathematical Institute of the Hungarian Academy of Sciences.
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."
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
Table of Contents
4. The laws of chance
Appendixes A and B