Fourier's Theorem/Integral Form

Theorem
Let $f: \R \to \R$ be a real function which is Lebesgue integrable.

Then:
 * $\displaystyle \map f t = \int_{-\infty}^\infty e^{2 \pi i t s} \paren {\int_{-\infty}^\infty e^{-2 \pi i d t} \map f t \rd t} \rd s$