0510321 20240103222822.220191104235959.9 5 s. P cav_un_epca*0509112978-80-7378-400-3145-149PrahaMatfyzPress2019InuiguchiMasahiroJiroušekRadimKratochvílVáclav probability measures inductive linear topology topological vector space cav_un_auth*0234872 Department of Decision Making Theory 100 Pištěk Miroslav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ K Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2019/MTR/pistek-0510321.pdf cav_un_auth*0348851 GA17-08182S GA ČR A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the classical (algebraic) case. Equipping a linear vector space with the so-called inductive linear topology, we derive the algebraic SSB representation on a topological basis, thus weakening the convexity assumption. Such a unifying approach to SSB representation permits also to fully discuss the relationship of topological and algebraic axioms of continuity, and leads to a stronger existence result for a maximal element. By applying this theory to probability measures we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems in this context. cav_un_auth*0381903 Czech-Japan Seminar on Data Analysis and Decision Making 2019 (CJS’19) /22./ 20190925 20190928 Nový Světlov CZ BA 10000 10100 10101 2020 1 PR RVO:67985556 http://hdl.handle.net/11104/0302533 S 2019 SCOPUS PUBMED WOS cav_un_epca*0509112 Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making (CJS’19) MatfyzPress 2019 Praha 145 149 978-80-7378-400-3 340 Inuiguchi Masahiro 340 Jiroušek Radim 340 Kratochvíl Václav