URN to cite this document: urn:nbn:de:bvb:703epub55448
Title data
Baier, Robert ; Farkhi, Elza:
Integration and Regularity of SetValued 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 GSpoints. In this way, a representation of a setvalued map with convex compact images is constructed by GSselections (which are defined by the GSpoints of its images). The properties of the GSpoints allow to represent Minkowski sum, Demyanov difference and Demyanov distance between sets in terms of their GSpoints, as well as the Aumann integral of a setvalued map is represented by the integrals of its GSselections. Regularity properties of setvalued maps (measurability, Lipschitz continuity, bounded variation) are reduced to the corresponding uniform properties of its GSselections. This theory is applied to formulate regularity conditions for the firstorder of convergence of iterated setvalued quadrature formulae approximating the Aumann integral.
Further data
Item Type:  Preprint, postprint 

Additional notes (visible to public):  Erscheint in: SetValued Analysis. Bd. 15 (März 2007) Heft 2 .  S. 185207 
Keywords:  Generalized Steiner selections; Demyanov distance; Aumann integral; Castaing representation; Setvalued 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:703epub55448 
Date Deposited:  19 May 2021 06:10 
Last Modified:  17 Jun 2021 09:29 
URI:  https://epub.unibayreuth.de/id/eprint/5544 