PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2002 | 153 | 3 | 235-247
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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.
Słowa kluczowe
Twórcy
  • Department of Mathematics, University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
  • Faculty of Mathematics, Łódź University, Stefana Banacha 22, 90-238 Łódź, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.