The law of large numbers for the max-scheme in Banach lattices
Author:
I. K. Matsak
Translated by:
N. N. Semenov
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
Full-text PDF Free Access
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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 $\mathsf E\| X \| < \infty$. Some generalizations of this proposition are considered.
References
- William Feller, An introduction to probability theory and its applications. Vol. II., 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403
- Edith Mourier, Eléments aléatoires dans un espace de Banach, Ann. Inst. H. Poincaré 13 (1953), 161–244 (French). MR 64339
- Michel Ledoux and Michel Talagrand, Probability in Banach spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 23, Springer-Verlag, Berlin, 1991. Isoperimetry and processes. MR 1102015
- Ī. K. Matsak, A remark on the ordered law of large numbers, Teor. Ĭmovīr. Mat. Stat. 72 (2005), 84–92 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 72 (2006), 93–102. MR 2168139, DOI https://doi.org/10.1090/S0094-9000-06-00667-3
- Ī. K. Matsak, Estimates for the moments of the supremum of normed sums of independent random variables, Teor. Ĭmovīr. Mat. Stat. 67 (2002), 104–116 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 67 (2003), 115–128. MR 1956624
- J.-P. Kahane, Some Random Series of Functions, D. C. Heath and Company, Lexington, Massachusetts, 1968. MR 0254888 (40:8095)
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
References
- 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)
- E. Mourier, Eléments aléatoires dans un espace de Banach, Ann. Inst. H. Poincaré 19 (1953), 161–244. MR 0064339 (16:268a)
- M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin, 1991. MR 1102015 (93c:60001)
- 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)
- 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)
- J.-P. Kahane, Some Random Series of Functions, D. C. Heath and Company, Lexington, Massachusetts, 1968. MR 0254888 (40:8095)
- 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
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
