Continuity of multifunctions characterized by Steiner selections

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider set-valued mappings defined on a topological space with closed convex images Rn. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise fills up the graph of the multifunction. Our aim is to construct a Castaing representation that characterizes Hausdorff continuity of the multifunction. The construction uses generalized Steiner points.

Original languageEnglish (US)
Pages (from-to)1985-1996
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume47
Issue number3
DOIs
StatePublished - Aug 1 2001

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Measurable Selection
Steiner Point
Measurability
Set-valued Mapping
Topological space
Countable
Closed
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Continuity of multifunctions characterized by Steiner selections. / Dentcheva Ruszczynski, Darinka.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 3, 01.08.2001, p. 1985-1996.

Research output: Contribution to journalArticle

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