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