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.
|Number of pages||12|
|Journal||Real Analysis Exchange|
|Publication status||Published - 2009|
All Science Journal Classification (ASJC) codes
- Geometry and Topology