Markov-Kakutani Theorem and Haar Measure

A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.

Notes on Measure and Integration in Locally Compact Spaces

This is a set of lecture notes which present an economical development of measure theory and integration in locally compact Hausdorff spaces. We have tried to illuminate the more difficult parts of the subject. The Riesz-Markov theorem is established in a form convenient for applications in modern analysis, including Haar measure on locally compact groups or weights on C∗-algebras...though appl...

Attractiveness of the Haar measure for linear cellular automata on Markov subgroups

For the action of an algebraic cellular automaton on a Markov subgroup, we show that the Cesàro mean of the iterates of a Markov measure converges to the Haar measure. This is proven by using the combinatorics of the binomial coefficients on the regenerative construction of the Markov measure.

Central and Local Limit Theories in Markov Dependent Random Variables

Limit Measures for A ne Cellular Automata

Let M be a monoid (e. is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A M ?! A M that commutes with all shift maps. Let be a (possibly nonstationary) probability measure on A M ; we develop suucient conditions on and F so that the sequence fF N g 1 N=1 weak*-converges to the Haar measure on A M , in density (and thus, in Cess aro average as we...