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Integration and Regularity of Set-Valued Maps Represented by Generalized Steiner Points

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005544
URN zum Zitieren der Version auf EPub Bayreuth: urn:nbn:de:bvb:703-epub-5544-8

Titelangaben

Baier, Robert ; Farkhi, Elza:
Integration and Regularity of Set-Valued Maps Represented by Generalized Steiner Points.
Bayreuth , 2006

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Abstract

A family of probability measures on the unit ball in |Rn generates a family of generalized Steiner (GS-)points for every convex compact set in |Rn. Such a "rich" family of probability measures determines a representation of a convex compact set by GS-points. In this way, a representation of a set-valued map with convex compact images is constructed by GS-selections (which are defined by the GS-points of its images). The properties of the GS-points allow to represent Minkowski sum, Demyanov difference and Demyanov distance between sets in terms of their GS-points, as well as the Aumann integral of a set-valued map is represented by the integrals of its GS-selections. Regularity properties of set-valued maps (measurability, Lipschitz continuity, bounded variation) are reduced to the corresponding uniform properties of its GS-selections. This theory is applied to formulate regularity conditions for the first-order of convergence of iterated set-valued quadrature formulae approximating the Aumann integral.

Weitere Angaben

Publikationsform: Preprint, Postprint
Zusätzliche Informationen (öffentlich sichtbar): Erscheint in: Set-Valued Analysis. Bd. 15 (März 2007) Heft 2 . - S. 185-207
Keywords: Generalized Steiner selections; Demyanov distance; Aumann integral; Castaing representation; Set-valued maps; Arithmetic set operations
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-5544-8
Eingestellt am: 19 Mai 2021 06:10
Letzte Änderung: 17 Jun 2021 09:29
URI: https://epub.uni-bayreuth.de/id/eprint/5544

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