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Theory of Probability and Mathematical Statistics

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The ordinal convergence and Glivenko-Cantelli type theorems in $ L_p(-\infty,\infty)$

Author: I. K. Matsak
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 83-92
MSC (2000): Primary 60B12
Published electronically: January 24, 2008
MathSciNet review: 2321183
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Abstract: Let $ F (t)$ be a distribution function and $ F_n (t)$ the corresponding empirical distribution function. We find necessary and sufficient conditions for the ordinal convergence o-lim$ F_n=F $ in the spaces $ L_p (-\infty,\infty)$.

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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, Kyiv 03127, Ukraine

Keywords: Empirical distribution function, ordinal convergence, Glivenko--Cantelli theorem
Received by editor(s): September 1, 2005
Published electronically: January 24, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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