1. Introductory Chapter.- 2. Extensions of the First Borel-Cantelli Lemma.- 3. Variants of the Second Borel-Cantelli Lemma.- 4. A Strengthened Form of the Second Borel-Cantelli Lemma.- 5. Conditional Borel-Cantelli Lemmas.- 6. Miscellaneous Results.
Tapas Kumar Chandra is a Professor of Statistics at the Indian Statistical Institute, Kolkata, India, since 1991. He is the author of the text books A First Course in Asymptotic Theory of Statistics and A First Course in Probability Theory. Among the problems solved by him, mention must be made of the age-old problems of finding valid Edgeworth expansions of the Likelihood Ratio Statistic and other perturbed Chi-square variables under very general conditions, and of comparing Bahadur-optimal test statistics, settling the conjecture of C. R. Rao on the optimality of score test for local alternatives and obtaining very general extensions of the Kolmogorov-Etemadi SLLN, the Marcinkiewicz-Zygmund SLLN, the well known results on the L1 and Lp convergence of the normalized sample sum and an inequality of Kolmogorov. His work is co-authored with J. K. Ghosh, R. R. Bahadur, S. Ghosal, R. Mukherjee, and others.
From the reviews: "This book is devoted to the famous Borel-Cantelli lemmas, which play a very important role in probability theory, in particular in limit theorems. ... The monograph is very well written, full of illustrating examples and problems ... . At the end of each chapter there is a complete ... list of references. It is a real pleasure to read this book. This monograph may be recommended not only for researchers but also for intermediate and graduate students." (Przemyslaw Matula, Mathematical Reviews, April, 2013)
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