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2015 Integration theory for vector valued functions and the Radon--Nikodym Theorem in the non-archimedean context
José N. Aguayo, Camilo G. Pérez
Banach J. Math. Anal. 9(2): 96-113 (2015). DOI: 10.15352/bjma/09-2-8

Abstract

In this paper we define non-archimedean measures and integral operators taking values in a locally convex space. We show the relation between these two concept. We define what we called integral function respect to an integral operator. We give necessary and sufficient condition in order to know when a function is integrable with respect to an integral operator. In the second part, we define a kind of absolutely continuous relation between measures in this context. After that, we formulate a type of Radon--Nikodym Theorem between vector measures and a scalar measures which are absolutely continuous.

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José N. Aguayo. Camilo G. Pérez. "Integration theory for vector valued functions and the Radon--Nikodym Theorem in the non-archimedean context." Banach J. Math. Anal. 9 (2) 96 - 113, 2015. https://doi.org/10.15352/bjma/09-2-8

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1312.28013
MathSciNet: MR3296108
Digital Object Identifier: 10.15352/bjma/09-2-8

Subjects:
Primary: 28B05
Secondary: 28C15, 47G10

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 2 • 2015
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