On lower and upper bounds for probabilities of unions and the Borel-Cantelli lemma-Reference-Cited by-同舟云学术

On lower and upper bounds for probabilities of unions and the Borel-Cantelli lemma

Published:2015-03-01 Issue:1 Volume:52 Page:102-128
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
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Author:

Frolov Andrei¹

Affiliation:

1. 1 St. Petersburg State University Dept. of Mathematics and Mechanics St. Petersburg Russia

Abstract

We obtain new lower and upper bounds for probabilities of unions of events. These bounds are sharp. They are stronger than earlier ones. General bounds may be applied in arbitrary measurable spaces. We have improved the method that has been introduced in previous papers. We derive new generalizations of the first and second parts of the Borel-Cantelli lemma.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://akademiai.com/doi/pdf/10.1556/sscmath.52.2015.1.1304

Reference22 articles.

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3. A lower bound on the probability of a union;Caen D.;Discrete Math.,1997

4. The Borel-Cantelli Lemma

5. On the application of the Borel-Cantelli lemma;Chung K. L.;Trans. Amer. Math. Soc.,1952

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