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We define entropy pairs for an invariant measure µ on a topological dynamical system ( X , T ), and show they allow one to construct the maximal topological factorwith entropy 0 for µ. Then we prove that for any µ, a µ-entropy pair is always topologically so, and the reverse is true when ( X , T ) is uniquely ergodic.
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Blanchard et al. (1995) studied this question.
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