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- Title
A STRUCTURAL THEOREM FOR METRIC SPACE VALUED MAPPINGS OF Φ-BOUNDED VARIATION.
- Authors
Maniscalco, Caterina
- Abstract
In this paper we introduce the notion of Φ-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 Φ-bounded variation. As an application we show that each mapping of Φ-bounded variation defined on a subset of ℝ possesses a Φ-variation preserving extension to the whole real line.
- Subjects
CALCULUS of variations; METRIC spaces; MATHEMATICAL mappings; SET theory; MATHEMATICAL functions; SCHRAMM, M.
- Publication
Real Analysis Exchange, 2010, Vol 35, Issue 1, p79
- ISSN
0147-1937
- Publication type
Article
- DOI
10.14321/realanalexch.35.1.0079