Filter exhaustiveness and filter limit theorems for -triangular lattice group-valued set functions

  • Antonio Boccuto

    Università degli Studi di Perugia, Italy
  • Xenofon Dimitriou

    University of Athens, Greece
Filter exhaustiveness and filter limit theorems for $k$-triangular lattice group-valued set functions cover

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Abstract

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. 379–389

DOI 10.4171/RLM/852