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A strong law of large numbers for generalized random sets from the viewpoint of empirical processes
Author(s):
Frank
N.
Proske;
Madan
L.
Puri
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2937-2944.
MSC (2000):
Primary 60D05;
Secondary 03E72
Posted:
January 8, 2003
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Additional information
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.
References:
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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:
10.1090/S0002-9939-03-06842-4
PII:
S 0002-9939(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
Posted:
January 8, 2003
Communicated by:
Claudia M. Neuhauser
Copyright of article:
Copyright
2003,
American Mathematical Society
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