Localized Transfunctions

Keywords

Generalized function; Localized transfunction; Measure-preserving transformation; Transfunction

Abstract

Generalized functions, called transfunctions, are defined as maps between spaces of measures on measurable spaces (X,σX) and (Y,σY). Measurable functions f: (X,σX) → (Y,σY ) can be identified with transfunctions via the push forward operator f#(μ)(B) = μ(f-1(B)). In this paper we introduce the notion of localization of transfunctions that gives an insight into which transfunctions arise from continuous functions or measurable functions or are close to such functions. We also introduce the notion of a graph of a transfunction and describe what it tells us about the transfunction. In our investigation of transfunctions, we are motivated by applications that include Monge-Kantorovich transportation problems and population dynamics.

Publication Date

1-1-2018

Publication Title

International Journal of Applied Mathematics

Volume

31

Issue

6

Number of Pages

689-707

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.12732/ijam.v31i6.1

Socpus ID

85067697870 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85067697870

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