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

V. V. Chistyakov, and A. Rychlewicz. "On the extension and generation of set-valued mappings of bounded variation." Studia Mathematica 153.3 (2002): 235-247. <http://eudml.org/doc/285320>.

@article{V2002,
abstract = {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.},
author = {V. V. Chistyakov, A. Rychlewicz},
journal = {Studia Mathematica},
keywords = {set-valued mappings; bounded variation; selections; extensions; generations},
language = {eng},
number = {3},
pages = {235-247},
title = {On the extension and generation of set-valued mappings of bounded variation},
url = {http://eudml.org/doc/285320},
volume = {153},
year = {2002},
}

TY - JOUR
AU - V. V. Chistyakov
AU - A. Rychlewicz
TI - On the extension and generation of set-valued mappings of bounded variation
JO - Studia Mathematica
PY - 2002
VL - 153
IS - 3
SP - 235
EP - 247
AB - 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.
LA - eng
KW - set-valued mappings; bounded variation; selections; extensions; generations
UR - http://eudml.org/doc/285320
ER -