Generalized convergence theorems for monotone measures

0545166 - ÚTIA 2022 RIV NL eng J - Journal Article
Li, J. - Ouyang, Y. - Mesiar, Radko
Generalized convergence theorems for monotone measures.
Fuzzy Sets and Systems. Roč. 412, č. 1 (2021), s. 53-64. ISSN 0165-0114. E-ISSN 1872-6801
Institutional support: RVO:67985556
Keywords : Absolute continuity * Egoroff's theorem * Lebesgue's theorem * Non-additive measure * Riesz's theorem
OECD category: Pure mathematics
Impact factor: 4.462, year: 2021
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0321916