FUNDAMENTALS OF PROBABILITY THEORY is a text comprising the major theorems of Probability and its Measure theoretic foundations. The main topics covered are independence, interchangeability. No prior knowledge of measure theory is assumed, and a unique feature of the book is the combined presentation of measure and probability. Special features include: An up-to-date treatment of U-statistics, a comprehensive treatment of the law of iterated logarithm, Infinitely divisible and stable laws, complete treatment of Borel-cantelli lemmas and laws of large numbers.
Tapas Kumar Chandra: Bayesian and Interdisciplinary Research Unit (BIRU), Indian Statistical Institute, Kolkata Sreela Gangopadhyay: CR Rao Advanced Institute of Mathematics, CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad
Families of Sets and Measures / Extensions of Measures and Lebesgue Integration / Product Spaces and Measures / Differentiation / Further Topics in Measure Theory / Laws of Large Numbers / Weak Convergence / Characteristic Functions / Central Limit Theorems / Discrete Time Markov Chains / Infinitely Divisible and Stable Laws / Law of Iterated Logarithms.