scholarly journals THE CONDITIONAL BOREL-CANTELLI LEMMA AND APPLICATIONS

2017 ◽  
Vol 54 (2) ◽  
pp. 441-460
Author(s):  
Qianmin Chen ◽  
Jicheng Liu
Keyword(s):  
Cantelli Lemma

The Borel-Cantelli Lemma and Product-Sum Formulas

1978 ◽  
Vol 85 (5) ◽  
pp. 363-364
Author(s):  
Frederick Stern
Keyword(s):  
Cantelli Lemma

Dynamical borel-cantelli lemma for hyperbolic spaces

2006 ◽  
Vol 152 (1) ◽  
pp. 143-155 ◽  
Author(s):  
François Maucourant
Keyword(s):  
Hyperbolic Spaces ◽  
Cantelli Lemma

A counterpart of the Borel–Cantelli lemma

1980 ◽  
Vol 12 (02) ◽  
pp. 281-282
Author(s):  
F. Thomas Bruss
Keyword(s):  
Cantelli Lemma

A counterpart of the Borel-Cantelli lemma

1980 ◽  
Vol 17 (4) ◽  
pp. 1094-1101 ◽  
Author(s):  
F. Thomas Bruss
Keyword(s):  
Random Walk ◽  
Probability Space ◽  
Branching Processes ◽  
Simple Random Walk ◽  
Cantelli Lemma ◽  
Sequence Of Events ◽  
Independence Condition ◽  
General Part

The general part of the Borel-Cantelli lemma says that for any sequence of events (An) defined on a probability space (Ω, Σ, P), the divergence of ΣnP(An) is necessary for P(An i.o.) to be one (see e.g. [1]). The sufficient direction is confined to the case where the An are independent. This paper provides a simple counterpart of this lemma in the sense that the independence condition is replaced by for some . We will see that this property of (An) may frequently be assumed without loss of generality. We also disclose a useful duality which allows straightforward conclusions without selecting independent sequences. A simple random walk example and a new result in the theory of ϕ -branching processes will show the tractability of the method.

Borel-Cantelli Lemma for Sugeno Measure

2014 ◽  
Vol 614 ◽  
pp. 367-370 ◽  
Author(s):  
Chun Qin Zhang ◽  
Hui Zhang
Keyword(s):  
Measure Space ◽  
Natural Extension ◽  
Fuzzy Measure ◽  
Cantelli Lemma ◽  
Sugeno Measure

Sugeno measure is a fuzzy measure. In this paper, we derive the Borel-Cantelli lemma for Sugeno measure. This result is a natural extension of the classical Borel-Cantelli lemma to the case where the measure tool is fuzzy. The properties of Sugeno measure are further discussed. Then the Borel-Cantelli lemma will be proven on Sugeno measure space. This work generalizes the research and applications of the Borel-Cantelli lemma.

scholarly journals A Short Note on the Conditional Borel-Cantelli Lemma

1978 ◽  
Vol 6 (4) ◽  
pp. 699-700 ◽  
Author(s):  
Louis H. Y. Chen
Keyword(s):  
Short Note ◽  
Cantelli Lemma

Comments on the paper: A bilateral inequality on the Borel–Cantelli Lemma

2009 ◽  
Vol 79 (7) ◽  
pp. 889-893 ◽  
Author(s):  
Shuhe Hu ◽  
Xuejun Wang ◽  
Xiaoqin Li ◽  
Yuanyuan Zhang
Keyword(s):  
Cantelli Lemma

scholarly journals A constructive Borel–Cantelli lemma. Constructing orbits with required statistical properties

2009 ◽  
Vol 410 (21-23) ◽  
pp. 2207-2222 ◽  
Author(s):  
Stefano Galatolo ◽  
Mathieu Hoyrup ◽  
Cristóbal Rojas
Keyword(s):  
Statistical Properties ◽  
Cantelli Lemma
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