The Demyanov metric and measurable multifunctions

• Autorzy: Leśniewski A.
• Języki publikacji: EN

Abstrakty

EN

We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.

Słowa kluczowe

EN

multifunctions; measurability; convex sets; bounded sets; Demyanov metric; Hausdorff metric

PL

wymierne wielofunkcyjne; zbiór wypukły; przestrzeń Hausdorffa

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 33
• Strony: 61--65
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Leśniewski A.

• Faculty of Mathematics & Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland,

Bibliografia

• [1] Baier R., Farkhi E., Differences of Convex Sets in the Space of Convex Compact Sets in the Space of Directed Sets. Part I: The Space of Directed Sets., Set-Valued Analysis, 9, 217-245, (2001).
• [2] Baier R., Farkhi E., Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points, Set-Valued Analysis, 15, 185-207, (2007).
• [3] Diamond P., Kloeden P., Rubinov A., Vladimirov A., Comparitive Properties of Three Metrics in the Space of Compact Convex Sets, Set-Valued Analysis 5, 267-289, (1997).
• [4] Leśniewski A., Rzeżuchowski T., The Demyanov Metric for Convex, Bounded Sets and Existence of Lipschitzan Selectors, Journal of Convex Analysis, 18(2011), No 3.
• [5] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Great Britain, (1993).