Banach Journal of Mathematical Analysis

Integration theory for vector valued functions and the Radon--Nikodym Theorem in the non-archimedean context

José N. Aguayo and Camilo G. Pérez

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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.

Article information

Banach J. Math. Anal., Volume 9, Number 2 (2015), 96-113.

First available in Project Euclid: 19 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10]
Secondary: 28C15: Set functions and measures on topological spaces (regularity of measures, etc.) 47G10: Integral operators [See also 45P05]

scalar and vector measures integral operators absolutely continuous measures


Aguayo, José N.; G. Pérez, Camilo. Integration theory for vector valued functions and the Radon--Nikodym Theorem in the non-archimedean context. Banach J. Math. Anal. 9 (2015), no. 2, 96--113. doi:10.15352/bjma/09-2-8.

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