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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Projectively bounded Fréchet measures


Author: Ron C. Blei
Journal: Trans. Amer. Math. Soc. 348 (1996), 4409-4432
MSC (1991): Primary 28B99, 46G10, 46A32; Secondary 43A05, 60G05
MathSciNet review: 1355069
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Abstract: A scalar valued set function on a Cartesian product of $\sigma $-algebras is a Fréchet measure if it is a scalar measure independently in each coordinate. A basic question is considered: is it possible to construct products of Fréchet measures that are analogous to product measures in the classical theory? A Fréchet measure is said to be projectively bounded if it satisfies a Grothendieck type inequality. It is shown that feasibility of products of Fréchet measures is linked to the projective boundedness property. All Fréchet measures in a two dimensional framework are projectively bounded, while there exist Fréchet measures in dimensions greater than two that are projectively unbounded. A basic problem is considered: when is a Fréchet measure projectively bounded? Some characterizations are stated. Applications to harmonic and stochastic analysis are given.


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Additional Information

Ron C. Blei
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: blei@uconnvm.uconn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01625-X
PII: S 0002-9947(96)01625-X
Received by editor(s): April 28, 1995
Article copyright: © Copyright 1996 American Mathematical Society