Let 𝜇 be *a finite complex valued measure* on $\mathbb{R}$ and let $\hat{\mu}$ be it's Fourier–Stieltjes transform \begin{align} \hat{\mu}(\omega)= \int_{\mathbb{R}} e^{it\omega} d \mu(t) \end{align} **Question:** Does $\hat{\mu}$ uniqueully determine $\mu$? I fairly sure that it does. However, I was not able to locate my standard references. Is there a good place where I can find proof of this fact?