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

The law of large numbers for the max-scheme in Banach lattices


Author: I. K. Matsak
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal: Theor. Probability and Math. Statist. 80 (2010), 111-117
MSC (2000): Primary 60B12
Published electronically: August 19, 2010
MathSciNet review: 2541956
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Abstract: We prove that the law of large numbers for the max-scheme in Banach lattices is equivalent to the condition that $ \E\Vert X \Vert < \infty $. Some generalizations of this proposition are considered.


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Additional Information

I. K. Matsak
Affiliation: Department of Operations Research, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kiev 03127, Ukraine
Email: mik@unicyb.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2010-00798-8
PII: S 0094-9000(2010)00798-8
Keywords: Max-scheme, Banach lattices, law of large numbers
Received by editor(s): April 10, 2008
Published electronically: August 19, 2010
Article copyright: © Copyright 2010 American Mathematical Society