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A structural approach to solving the 6th Hilbert problem
Author(s):
Yu.
I.
Petunin;
D.
A.
Klyushin
Translated by:
V. Zayats
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 71
(2004).
Journal:
Theor. Probability and Math. Statist.
No. 71
(2005),
165-179.
MSC (2000):
Primary 60A05
Posted:
December 30, 2005
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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).
References:
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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:
10.1090/S0094-9000-05-00656-3
PII:
S 0094-9000(05)00656-3
Received by editor(s):
17/DEC/2001
Posted:
December 30, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
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