Filter exhaustiveness and filter limit theorems for $k$-triangular lattice group-valued set functions
Antonio Boccuto, Xenofon Dimitriou · Rendiconti Lincei Matematica e Applicazioni · 2019
We give some limit theorems for sequences of lattice group-valued k -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 (s) -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.