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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Independence and atoms


Authors: Gábor J. Székely and Tamás F. Móri
Journal: Proc. Amer. Math. Soc. 130 (2002), 213-216
MSC (2000): Primary 60A10
Published electronically: April 25, 2001
MathSciNet review: 1855639
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Abstract: We prove that if the range of a probability measure $P$ contains an interval $[0,\varepsilon ]$, $\varepsilon >0$, then there are infinitely many (nontrivial) independent events in this probability space.


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Additional Information

Gábor J. Székely
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221 and Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O.B. 127, 1364 Budapest, Hungary
Email: gabors@bgnet.bgsu.edu

Tamás F. Móri
Affiliation: Department of Probability and Statistics, Eötvös L. University, Kecskeméti u. 10,1093 Budapest, Hungary
Email: moritamas@ludens.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06045-2
PII: S 0002-9939(01)06045-2
Keywords: Independence, atom, purely atomic probability measure, Borel-Cantelli lemma, range of a probability measure
Received by editor(s): July 15, 1999
Received by editor(s) in revised form: May 24, 2000
Published electronically: April 25, 2001
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society