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For the action of an algebraic cellular automaton on a Markov subgroup, weshow that the Ces\`{a}ro mean of the iterates of a Markov measure converges tothe Haar measure. This is proven by using the combinatorics of the binomialcoefficients on the regenerative construction of the Markov measure.

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