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Probability Theory by S.R.S Varadhan (New York University, Courant Institute of Mathematical Sciences, USA) (Paperback, 2001)

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Author: S.R.S Varadhan. In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem.