On the extension and generation of set-valued mappings of bounded variation

• Autorzy: V. V. Chistyakov , A. Rychlewicz
• Języki publikacji: EN

Abstrakty

EN

We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated set-valued mappings and show that, under suitable assumptions, set-valued mappings (with arbitrary domains) which are Lipschitzian, of bounded variation or absolutely continuous are generated by certain families of mappings with nice properties. Finally, we prove a Castaing type representation theorem for set-valued mappings of bounded variation.

Kategorie tematyczne

• 26A45: Functions of bounded variation, generalizations
• 54C60: Set-valued maps
• 26A16: Lipschitz (H\"older) classes
• 26A51: Convexity, generalizations
• 54E50: Complete metric spaces
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 3
• Strony: 235-247

Daty

wydano

2002

Twórcy

autor

V. V. Chistyakov

• Department of Mathematics, University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia

autor

A. Rychlewicz

• Faculty of Mathematics, Łódź University, Stefana Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/sm153-3-2