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Let $f$ be a Lebesgue integrable function. A point $x$ in the domain of $f$ is a Lebesgue point if $f(x)=\lim_{r\to 0}\frac{1}{2r}\int_{x-r}^{x+r} f(y) dy$. How can I prove that $\sin x$ and $\cos x$ have common Lebesgue point in (0;1)?

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