Prove that if \(F(x)\) is a distribution and \(f(t)\) the corresponding characteristic function, then for any value of \(x\) the equation

\[ \lim _{T \rightarrow \infty} \frac{1}{2 T} \int_{-T}^{T} f(t) e^{-i t x} d t=F(x+0)-F(x-0) \]

holds.