0545166 20220328124748.220210903235959.9 000637966800004 85089189678 10.1016/j.fss.2020.07.020 12 s. P cav_un_epca*02566420165-01144121 (2021)53-64Elsevier Absolute continuity Egoroff's theorem Lebesgue's theorem Non-additive measure Riesz's theorem cav_un_auth*0348640 Li J. CN 35 K cav_un_auth*0258953 Ouyang Y. CN 35 cav_un_auth*0101163 Mesiar Radko UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics 30 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2021/E/mesiar-0545166.pdf https://www.sciencedirect.com/science/article/pii/S0165011415002894?via%3Dihub In this paper, we propose three types of absolute continuity for monotone measures and present some of their basic properties. By means of these three types of absolute continuity, we establish generalized Egoroff's theorem, generalized Riesz's theorem and generalized Lebesgue's theorem in the framework involving the ordered pair of monotone measures. The Egoroff theorem, the Riesz theorem and the Lebesgue theorem in the traditional sense concerning a unique monotone measure are extended to the general case. These three generalized convergence theorems include as special cases several previous versions of Egoroff-like theorem, Riesz-like theorem and Lebesgue-like theorem for monotone measures. WOS BA 10000 10100 10101 2022 3 RVO:67985556 http://hdl.handle.net/11104/0321916 S 2 Article Computer Science Theory Methods|Mathematics Applied|Statistics Probability C MATHEMATICS.APPLIED|COMPUTERSCIENCE.THEORY&METHODS|STATISTICS&PROBABILITY 3.581 1.845 19.1 0.0068 0.7 19849 191 1.338 36.42 4.31 2405 Q1 3.889 239 Q1 91.4 Q2 Q2 1.83 Q1 97.94 2021 85089189678 SCOPUS PUBMED 000637966800004 WOS cav_un_epca*0256642 Fuzzy Sets and Systems 0165-0114 1872-6801 Roč. 412 č. 1 2021 53 64 Elsevier