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I am having trouble with the following question.

Let $\mu$ be finite measure on $\mathbb{R}$ and let $\hat{\mu}(\xi) = \int_{-\infty}^\infty e^{-ix \xi} d\mu(x)$ be its Fourier transform. Prove that

$$|\mu(\{x\})| \le \limsup_{|\xi| \rightarrow \infty} |\hat{\mu}(\xi)|$$

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