Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-01-06045-2
Published electronically: April 25, 2001
MathSciNet review: 1855639
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. Borkar, V. S. (1995).
    Probability Theory,
    Springer-Verlag, New York. MR 98e:60001
  • 2. Billingsley, P. (1995).
    Probability and Measure, 3rd ed.
    J. Wiley & Sons, New York. MR 95k:60001
  • 3. Chen, Zh., Rubin, H., Vitale, R. A. (1997). Independence and determination of probabilities, Proc. Amer. Math. Soc., 125 no. 12, 3721-3723. MR 98b:60007
  • 4. Rényi, A. (1970).
    Probability Theory,
    North-Holland, New York. MR 47:4296

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60A10

Retrieve articles in all journals with MSC (2000): 60A10


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: https://doi.org/10.1090/S0002-9939-01-06045-2
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

American Mathematical Society