This book shares the dictum of J. L. Doob in treating probability theory as a branch of measure theory and establishes this relationship early. Probability measures in product spaces are introduced right at the start as a way of laying the groundwork to later claim the existence of stochastic processes with prescribed finitedimensional distributions. Other topics analyzed in the book include supports of probability measures, zeroone laws in product measure spaces, the ErdösKac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a textbook for students pursuing graduate programs in mathematics and/or statistics. The book aims to help teachers present the theory with ease and to help students sustain their interest and joy in learning the subject. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Students interested in mathematics and/or statistics. Table of Contents  Probability measures in product spaces
 Weak convergence of probability measures
 Characteristic functions
 Independence
 The central limit theorem and its ramifications
 The law of the iterated logarithm
 Discrete time Markov chains
 Index
