Editing Fourier inversion theorem (section)

===Integrable functions with integrable Fourier transform===

The Fourier inversion theorem holds for all continuous functions that are absolutely integrable (i.e. <math>L^1(\mathbb R^n)</math>) with absolutely integrable Fourier transform. This includes all Schwartz functions, so is a strictly stronger form of the theorem than the previous one mentioned. This condition is the one used above in the [[#Statement|statement section]].

A slight variant is to drop the condition that the function <math>f </math> be continuous but still require that it and its Fourier transform be absolutely integrable. Then <math>f = g</math> [[almost everywhere]] where {{math|''g''}} is a continuous function, and <math>\mathcal{F}^{-1}(\mathcal{F}f)(x)=g(x)</math> for every <math>x \in \mathbb R^n</math>.