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1989/1990 Change of variable in the semigroup valued refinement integral
Isidore Fleischer
Real Anal. Exchange 15(1): 106-110 (1989/1990). DOI: 10.2307/44151995

Abstract

The standard change of variable formula, for T measurable from a measure space (S,S,λ) to a measurable space (S¯,S¯) on which a measurable t¯ is defined (see e.g.[H]), St¯Tdλ=S¯t¯d(λT1), is developed for a semigroup valued refinement integral. (The integral on the right can be rewritten in “Jacobian” form, S¯t¯dλT1dλ¯dλ¯, when λT1 is differentiable with respect to a measure λ¯ on S¯; the attempt in [DS] Lemma III.10.8 to develop the result by starting from λ¯ is incorrect). This yields a result for the order-convergent integral of real-valued integrands against positive finitely additive measures in an Archimedian ordered vector space as well as a (correct) result for the [DS] Banach space valued integral of a vector valued integrand against a real-valued finitely additive measure.

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Isidore Fleischer. "Change of variable in the semigroup valued refinement integral." Real Anal. Exchange 15 (1) 106 - 110, 1989/1990. https://doi.org/10.2307/44151995

Information

Published: 1989/1990
First available in Project Euclid: 11 April 2022

Digital Object Identifier: 10.2307/44151995

Rights: Copyright © 1989 Michigan State University Press

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Vol.15 • No. 1 • 1989/1990
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