The gap between probability and prevalence: Loneliness in vector spaces
Author:
Maxwell B. Stinchcombe
Journal:
Proc. Amer. Math. Soc. 129 (2001), 451457
MSC (1991):
Primary 28C20, 60B11; Secondary 90B40
Published electronically:
July 27, 2000
MathSciNet review:
1694881
Fulltext PDF Free Access
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Abstract: The best available definition of a subset of an infinite dimensional, complete, metric vector space being ``small'' is Christensen's Haar zero sets, equivalently, Hunt, Sauer, and Yorke's shy sets. The complement of a shy set is a prevalent set. There is a gap between prevalence and likelihood. For any probability on , there is a shy set with . Further, when is locally convex, any i.i.d. sequence with law repeatedly visits neighborhoods of only a shy set of points if the neighborhoods shrink to at any rate.
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Additional Information
Maxwell B. Stinchcombe
Affiliation:
Department of Economics, University of Texas at Austin, Austin, Texas 787121173
Email:
maxwell@eco.utexas.edu
DOI:
http://dx.doi.org/10.1090/S000299390005543X
PII:
S 00029939(00)05543X
Received by editor(s):
March 1, 1999
Received by editor(s) in revised form:
April 19, 1999
Published electronically:
July 27, 2000
Communicated by:
Claudia Neuhauser
Article copyright:
© Copyright 2000
American Mathematical Society
