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Theory of Probability and Mathematical Statistics

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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
DOI: https://doi.org/10.1090/S0094-9000-2010-00798-8
Published electronically: August 19, 2010
MathSciNet review: 2541956
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Abstract | References | Similar Articles | Additional Information

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.


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

  • 1. W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403 (42:5292)
  • 2. E. Mourier, Eléments aléatoires dans un espace de Banach, Ann. Inst. H. Poincaré 19 (1953), 161-244. MR 0064339 (16:268a)
  • 3. M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. MR 1102015 (93c:60001)
  • 4. I. K. Matsak, Some remarks on the ordinal strong law of large numbers, Teor. Imovirnost. Matem. Statist. 72 (2005), 84-92; English transl. in Theory Probab. Math. Statist. 72 (2006), 93-102. MR 2168139 (2006f:60011)
  • 5. I. K. Matsak, Estimates for the moments of the supremum of normalized sums of independent random variables, Teor. Imovirnost. Matem. Statist. 67 (2002), 104-116; English transl. in Theory Probab. Math. Statist. 67 (2003), 115-128. MR 1956624 (2004i:60061)
  • 6. J.-P. Kahane, Some Random Series of Functions, D. C. Heath and Company, Lexington, Massachusetts, 1968. MR 0254888 (40:8095)
  • 7. G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, UK, 1952. MR 0046395 (13:727e)

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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: https://doi.org/10.1090/S0094-9000-2010-00798-8
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

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