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Let $(I,B,\mu)$ be the standard probability space with $I=[0,1]$ , $B=$ Borel sets, and $\mu$ is Lebesgue measure. Now, for each $n\in N$, let $F_n$ be the rotation $F_n(x)=x+1/n \pmod 1$. Is it correct that for every Borel set $E$ , $ \mu (F_nE\;\triangle\; E)\to0$ as $n\to \infty$?

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