caa a22 4500 463205944 CHVBK 20180405153126.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11228-006-0032-6 doi (NATIONALLICENCE)springer-10.1007/s11228-006-0032-6 Hess Christian Centre de Recherche Stratégies et Dynamiques Financières, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, CEDEX 16, France aut On the Parametrized Integral of a Multifunction: The Unbounded Case [Elektronische Daten] [Christian Hess] Integration of set-valued maps (alias multifunctions) depending on a parameter is revisited. Results of Artstein, and of Saint-Pierre and Sajid are extended to the case of set-valued maps whose values may be unbounded. In the general case, this is achieved assuming that the transition probabilities involved in the integration procedure are absolutely continuous with respect to some fixed probability measure. However, when the integrating probability measure does not depend on the parameter this hypothesis is shown to be unnecessary. On the other hand, an alternative proof of a result of Saint-Pierre and Sajid is provided for convex compact-valued multifunctions. An application is given to the control of chattering systems. It is an extension of a result of Artstein to the case of set-valued maps with unbounded values. The proof of the main results is simple and essentially relies on measurable selections arguments. Springer Science + Business Media B.V., 2006 set-valued maps nationallicence integration of multifunctions nationallicence Aumann integral nationallicence transition probability nationallicence measurable selections nationallicence chattering controls nationallicence Radon-Nikodym property nationallicence Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 1-20 0927-6947 15:1<1 2007 15 11228 https://doi.org/10.1007/s11228-006-0032-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11228-006-0032-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hess Christian Centre de Recherche Stratégies et Dynamiques Financières, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris, CEDEX 16, France aut NATIONALLICENCE 773 0- Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 1-20 0927-6947 15:1<1 2007 15 11228 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer