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Some remarks on the ordinal strong law of large numbers


Author: I. K. Matsak
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 93-102
MSC (2000): Primary 60B12
Published electronically: August 18, 2006
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Abstract: We prove that the ordinal law of large numbers and the law of large numbers in the norm are equivalent for Banach lattices that do not contain uniformly the space $ l_1^n$.


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Additional Information

I. K. Matsak
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: d.i.m.@ukrpost.net

DOI: https://doi.org/10.1090/S0094-9000-06-00667-3
Received by editor(s): January 15, 2004
Published electronically: August 18, 2006
Article copyright: © Copyright 2006 American Mathematical Society