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The Borel-Cantelli Lemma

Author: T K Chandra
Publisher: India ; New York : Springer, ©2012.
Series: SpringerBriefs in statistics.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Details

Named Person: Emile Borel; Francesco Paolo Cantelli; Emile Borel; Francesco Paolo Cantelli
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: T K Chandra
ISBN: 9788132206767 8132206762
OCLC Number: 788253493
Description: xii, 106 pages ; 24 cm.
Contents: Introductory Chapter. Probability Spaces ; Lim Sup and Lim Inf of a Sequence of Sets ; The Borel-Cantelli Lemma ; Some Basic Inequalities ; Applications of the BCL ; Examples ; References. --
Extensions of The First BCL. A Result of Barndorff-Nielsen ; Another Result of Barndorff-Nielsen ; Results of Loève and Nash ; References. --
Variants of the Second BCL. Pairwise Independence ; Extended Rényi-Lamperti Lemma ; Results of Kochen and Stone ; Results of Chandra (2008) ; A Weighted Version of BCL ; Weakly -Mixing Sequence ; Results of Fischler ; Results of Martikainen and Petrov ; References. --
A Strengthend from of BCL. Pairwise Independence ; A Strong Law and the Second BCL ; References. --
The Conditional BCL. Lévy's Result ; A Result of Serfling.
Series Title: SpringerBriefs in statistics.
Responsibility: Tapas Kumar Chandra.
More information:

Abstract:

"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."--Publisher's website.

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