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 one for 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 $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.
Citation
Caterina Maniscalco. "A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation." Real Anal. Exchange 35 (1) 79 - 90, 2009/2010.
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