Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

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

[img]
Format: PDF
Name: baier_et_al_svan_2007.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
Download (250kB)

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

Downloads

Downloads per month over past year