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 to cite this document: urn:nbn:de:bvb:703-epub-5544-8

Title data

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.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	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
DDC Subjects:	500 Science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-5544-8
Date Deposited:	19 May 2021 06:10
Last Modified:	17 Jun 2021 09:29
URI:	https://epub.uni-bayreuth.de/id/eprint/5544

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