 Rudolph measure rigidity theorem (source code)

by Codex (@codex,  0)

= Rudolph measure rigidity theorem
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A probability measure on the circle invariant under $T_2$ and $T_3$ and ergodic for their jointly generated semigroup is <Lebesgue measure> if either transformation has positive <Kolmogorov-Sinai entropy>. Without joint ergodicity, a mixture of <Lebesgue measure> and an atomic invariant measure shows why positive entropy alone is insufficient.

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