Compactness in Groups of Group-Valued Mappings

Diana Caponetti (), Alessandro Trombetta and Giulio Trombetta
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Diana Caponetti: Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Alessandro Trombetta: Department of Mathematics and Computer Science, University of Calabria, Ponte Pietro Bucci 31B, 87036 Rende, Italy
Giulio Trombetta: Department of Mathematics and Computer Science, University of Calabria, Ponte Pietro Bucci 31B, 87036 Rende, Italy

Mathematics, 2022, vol. 10, issue 21, 1-11

Abstract: We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Fréchet–Šmulian and Ascoli–Arzelà compactness criteria found in the literature.

Keywords: group; pseudonorm; convergence (and local convergence) in measure; measure of noncompactness; equimeasurability; uniform quasiboundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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