A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation

Caterina Maniscalco, Caterina Maniscalco

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Abstract

In this paper we introduce the notion of$\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the onefor real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\RB$possesses a $\Phi$-variation preserving extension to the whole real line.
Lingua originaleEnglish
pagine (da-a)79-90
Numero di pagine12
RivistaReal Analysis Exchange
Volume35
Stato di pubblicazionePublished - 2009

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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