6533b7d5fe1ef96bd1263e46

RESEARCH PRODUCT

Compactness in Groups of Group-Valued Mappings

Diana CaponettiAlessandro TrombettaGiulio Trombetta

subject

equimeasurabilitySettore MAT/05 - Analisi MatematicaGeneral Mathematicsuniform quasiboundednessComputer Science (miscellaneous)convergence (and local convergence) in measuremeasure of noncompactnessgroupgroup; pseudonorm; convergence (and local convergence) in measure; measure of noncompactness; equimeasurability; uniform quasiboundednesspseudonormEngineering (miscellaneous)

description

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.

yearjournalcountryeditionlanguage
2022-10-26Mathematics
https://doi.org/10.3390/math10213973