Is there a example $(X,f,\mu)$ such that $X$ is a closed subset of Euclidean space, $f$ be a quasi-symmetric mapping but not a Lipschitz mapping, $f(X)=X$, $\mu$ is a finite measure on $X$ that is invariant and ergodic under $f$.
Give a example about invariant ergodic measure and quasi-symmetric mapping
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measure-theory
ergodic-theory
invariant-theory
quasiconformal-maps