In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

we study harmonic analysis on cocommutative kpc-hyper-groups‎, which is a generalization of djs-hypergroups‎, ‎introduced by kalyuzhnyi‎, ‎podkolzin and chapovsky‎. ‎we prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a radon measure on kpc-hypergroup $q$ and $gamma$ is a character on $q$.

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the approximations of locally compact groups by more general finite algebraic systems are investigated. It is proved that the approximation of locally compact groups b...

Abstract Let and $H$?> be locally compact groups with fixed two-sided invariant Haar measures. A polyhomomorphism $G\rightarrowtail H$?> is a closed subgroup $R\subset G\times measure, whose marginals on are dominated by the measures . can regarded as multi-valued map sending points to sets equipped ‘uniform’ For two polyhomomorphisms ${G\rightarrowtail H}$?> $H\rightarrowtail K$?...