2020-01-25T18:22:51Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000403112019-12-24T07:27:15Z00312:06865:07055:0705600009:00504:06868:07057:07058
A Brooks Type Integral with Respect to a Set-Valued Measureenghttp://hdl.handle.net/2261/1534Departmental Bulletin PaperPrecupanu, Anca-MariaA generalization of the set--valued Brooks integral [3] with respect to a set--valued measure whose values are subsets of a Hausdorff locally convex topological vector space is presented. The construction of this new kind of integral is based on Weber's result [19] concerning the existence of a family of semi--invariant pseudo--metrics which ge\-ne\-ra\-tes the uniformity of a uniform semigroup (in our case, the semigroup of convex, bounded, closed subsets of a Hausdorff locally convex topological vector space). Several properties of the new integral are given and also a theorem of Vitali type is established.Journal of mathematical sciences, the University of Tokyo33533546199613405705AA11021653application/pdf415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40311&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14