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Integration with respect to vector valued Radon polymeasures

Part of: Set functions, measures and integrals with values in abstract spaces Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  09 April 2009

Brian Jefferies  and
Werner J. Ricker
Brian Jefferies
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W., Australia
Werner J. Ricker
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W., Australia
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Abstract

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Problems dealing with certain functional calculi for systems of non-commuting operators, and ordered calculi for systems of certain types of pseudo-differential operators, can sometimes be treated via the methods of integration with respect to polymeasures. The polymeasures arising in this fashion (called Radon polymeasures) often have additional structure not available in the general theory. This allows for a more extensive class of “integrable” functions than just the product functions allowed in the abstract theory. The purpose here is to further develop special aspects of integration with respect to Radon polymeasures with a particular emphasis on identifying large classes of “integrable” functions.

MSC classification

Secondary: 28B05: Vector-valued set functions, measures and integrals 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 1 , February 1994 , pp. 17 - 40
Copyright
Copyright © Australian Mathematical Society 1994

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