\begin{definition}[Definition:Fourier Transform/Real Function/Formulation 1]
Let $f: \R \to \R$ be a real function which is Lebesgue integrable.
The '''Fourier transform''' of $f$ is defined and denoted as:
:$\ds \map { \map \FF f } s = \map {\hat f} s := \int_{-\infty}^\infty e^{-2 \pi i s t} \map f t \rd t$
\end{definition}