Items related to Foundations of the Theory of Probability
Synopsis
This book provides a rigorous axiomatic foundation for the theory of probability, a field long considered peculiar within the realm of mathematics. Drawing on Lebesgue's groundbreaking theories of measure and integration, the author lays bare the fundamental concepts of probability, emphasizing analogies between measure and probability, and integrals and mathematical expectations. The work explores probability distributions in infinite-dimensional spaces, delves into the differentiation and integration of mathematical expectations with respect to parameters, and, most importantly, examines the theory of conditional probabilities and expectations. The book's sixth chapter offers a comprehensive survey of the limitations of the ordinary and strong law of large numbers, highlighting the work of A. Khinchine and the author. This book stands as a landmark in the development of probability theory, offering a robust and accessible axiomatic framework that continues to inform and inspire mathematicians and statisticians today.
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