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- Jun 20, 2014

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Consider a strictly increasing sequence of natural numbers $(n_k)_{k = 1}^\infty$, and suppose $X$ is the subset of $[0,2\pi]$ consisting of all $x$ such that the sequence $(\sin(n_k x))_{k = 1}^\infty$ is convergent. Prove $X$ has Lebesgue measure zero.

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