Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 28B99, 46G10, 46A32, 43A05, 60G05

Retrieve articles in all journals with MSC (1991): 28B99, 46G10, 46A32, 43A05, 60G05

Additional Information

Ron C. Blei
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Received by editor(s): April 28, 1995
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society