Let $X, Y \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number.

Then \begin{equation} \forall \, t \in \mathbb{R} : \mathbb{E}(e^{i t X}) = \mathbb{E}(e^{i t Y}) \quad \iff \quad X \overset{d}{=} Y \end{equation}