caa a22 4500 463206134 CHVBK 20180405153126.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11228-006-0038-0 doi (NATIONALLICENCE)springer-10.1007/s11228-006-0038-0 Regularity and Integration of Set-Valued Maps Represented by Generalized Steiner Points [Elektronische Daten] [Robert Baier, Elza Farkhi] A family of probability measures on the unit ball in $\mathbb{R}^{n}$ generates a family of generalized Steiner (GS-)points for every convex compact set in $\mathbb{R}^{n}$ . 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. Springer Science + Business Media B.V., 2007 Generalized Steiner selections nationallicence Demyanov distance nationallicence Aumann integral nationallicence Castaing representation nationallicence Set-valued maps nationallicence Arithmetic set operations nationallicence Baier Robert University of Bayreuth, Chair of Applied Mathematics, 95440, Bayreuth, Germany aut Farkhi Elza Tel Aviv University, School of Mathematical Sciences, Haim Levanon Street, 69978, Tel Aviv, Israel aut Set-Valued Analysis Kluwer Academic Publishers 15/2(2007-06-01), 185-207 0927-6947 15:2<185 2007 15 11228 https://doi.org/10.1007/s11228-006-0038-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11228-006-0038-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baier Robert University of Bayreuth, Chair of Applied Mathematics, 95440, Bayreuth, Germany aut NATIONALLICENCE 700 1- Farkhi Elza Tel Aviv University, School of Mathematical Sciences, Haim Levanon Street, 69978, Tel Aviv, Israel aut NATIONALLICENCE 773 0- Set-Valued Analysis Kluwer Academic Publishers 15/2(2007-06-01), 185-207 0927-6947 15:2<185 2007 15 11228 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer