Filter exhaustiveness and filter limit theorems for -triangular lattice group-valued set functions
Antonio BoccutoUniversità degli Studi di Perugia, Italy
Xenofon DimitriouUniversity of Athens, Greece
We give some limit theorems for sequences of lattice group-valued -triangular set functions, in the setting of filter convergence, and some results about their equivalence. We use the tool of filter exhaustiveness to get uniform -boundedness, uniform continuity and uniform regularity of a suitable subsequence of the given sequence, whose indexes belong to the involved filter. Furthermore we pose some open problems.
Cite this article
Antonio Boccuto, Xenofon Dimitriou, Filter exhaustiveness and filter limit theorems for -triangular lattice group-valued set functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 2, pp. 379–389DOI 10.4171/RLM/852