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The following fact about (row) stochastic matrices is an easy consequence of well known results: for each positive integer n>=1 there is a positive integer q=q(n) with the property that if A is any nxn stochastic matrix then the sequence of matrices A q ,A 2q ,A 3q ,... converges. We prove a generalization of this for sets of stochastic matrices under the Hausdorff...
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