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Proceedings of the American Mathematical Society

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A strong law of large numbers for generalized random sets from the viewpoint of empirical processes


Authors: Frank N. Proske and Madan L. Puri
Journal: Proc. Amer. Math. Soc. 131 (2003), 2937-2944
MSC (2000): Primary 60D05; Secondary 03E72
Published electronically: January 8, 2003
MathSciNet review: 1974352
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Abstract: In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.


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Additional Information

Frank N. Proske
Affiliation: Abt. Math. III, Universität Ulm, 89069 Ulm, Germany
Address at time of publication: Department of Mathematics, University of Oslo, 1053 Blindern, 0316 Oslo, Norway
Email: frproske@metronet.de, proske@math.uio.no

Madan L. Puri
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: puri@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06842-4
Keywords: Random set, fuzzy set, fuzzy random variable, embedding, Hausdorff distance, empirical process, strong law of large numbers.
Received by editor(s): March 12, 2002
Received by editor(s) in revised form: April 11, 2002
Published electronically: January 8, 2003
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2003 American Mathematical Society