The Borel-Cantelli Lemma

  • Tapas Kumar┬áChandra

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST, volume 2)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Tapas Kumar Chandra
    Pages 1-49
  3. Tapas Kumar Chandra
    Pages 51-62
  4. Tapas Kumar Chandra
    Pages 63-84
  5. Tapas Kumar Chandra
    Pages 85-93
  6. Tapas Kumar Chandra
    Pages 95-102
  7. Back Matter
    Pages 103-106

About this book

Introduction

This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.

Keywords

Measure Probability Set

Authors and affiliations

  • Tapas Kumar┬áChandra
    • 1
  1. 1., Applied Statistics DivisionIndian Statistical InstituteKolkataIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-81-322-0677-4
  • Copyright Information The Author(s) 2012
  • Publisher Name Springer, India
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-322-0676-7
  • Online ISBN 978-81-322-0677-4
  • Series Print ISSN 2191-544X
  • Series Online ISSN 2191-5458
  • About this book
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