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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

A structural approach to solving the 6th Hilbert problem


Authors: Yu. I. Petunin and D. A. Klyushin
Translated by: V. Zayats
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 165-179
MSC (2000): Primary 60A05
Published electronically: December 30, 2005
MathSciNet review: 2144329
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper deals with an approach to solving the 6th Hilbert problem based on interpreting the field of random events as a partially ordered set endowed with a natural order of random events obtained by formalization and modification of the frequency definition of probability. It is shown that the field of events forms an atomic generated, complete, and completely distributive Boolean algebra. The probability distribution of the field of events generated by random variables is studied. It is proved that the probability distribution generated by random variables is not a measure but only a finitely additive function of events in the case of continuous random variables (both rational- and real-valued).


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Additional Information

Yu. I. Petunin
Affiliation: National Taras Shevchenko University, Faculty of Cybernetics, Volodymyrs’ka Street 64, Kyïv 01033, Ukraine
Email: vm214@dcp.kiev.ua

D. A. Klyushin
Affiliation: National Taras Shevchenko University, Faculty of Cybernetics, Volodymyrs’ka Street 64, Kyïv 01033, Ukraine

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00656-3
PII: S 0094-9000(05)00656-3
Received by editor(s): December 17, 2001
Published electronically: December 30, 2005
Article copyright: © Copyright 2005 American Mathematical Society