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?

Let $\mu$ be a finite complex valued measure on $\mathbb{R}$ and let $\hat{\mu}$ be it's Fourier–Stieltjes transform $$ \hat{\mu}(\omega)= \int_{\mathbb{R}} e^{it\omega} d \mu(t) $$ Question: Does $\hat{\mu}$ uniquely determine $\mu$? I am 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?