I cannot prove the following equality on the Fourier transformation of measure:
let $\mu$ be a finite Borel measure on $R^d,$ then 
$$\lim\limits\_{T\to \infty}\frac{1}{(2T)^d}\int\_{[-T,T]^d}|\widehat{\mu}(\xi)|^2d\xi=\sum\_{x\in R^d}\mu(\{x\})^2,$$
where $\widehat{\mu}(\xi)=\int e^{-2\pi i\xi\cdot x}d\mu(x)$, i.e, the Fourier transformation of the measure $\mu.$


Anyone can help me? Many thanks!



How to prove the equality on the Fourier transformation of measure?
It's a classic theorem of Wiener ([1933, p. 146](https://books.google.com/books?id=L1U4AAAAIAAJ&pg=PA146)).


Modern expositions see e.g. [Katznelson 1968](http://www.ams.org/mathscinet-getitem?mr=248482) ([Chap 6](http://math.stanford.edu/~katznel/23309/index23309.html), Thm 2.12), [Strichartz 1990](http://www.ams.org/mathscinet-getitem?mr=1040961) (Thm 4.4), [Jaksic 2006](http://www.ams.org/mathscinet-getitem?mr=2248985) ([§2.5](http://www.math.mcgill.ca/jaksic/Papers.html), Thm 6).


