In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

let $fm(x)$ be the  space of  all finite regular borel measures on $x$. a general measure algebra is a subspace  of$fm(x)$,which is an $l$-space and has a multiplication preserving the probability measures. let $clsubseteqfm(x)$ be a general measure algebra on a locallycompact space $x$. in this paper, we investigate the relation between arensregularity of $cl$ and the topology of $x$. we  find...