Fourier's Theorem/Integral Form/Continuous Point

Theorem
Let $f: \R \to \R$ be a real function which satisfies the Dirichlet conditions on $\R$. Let $f$ be continuous at $t \in \R$.

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

Proof
At a point of continuity we have:

The result follows from Fourier's Theorem: Integral Form.