Let $X_1, \ldots, X_N \in \text{Random}(\mathbb{R}^D)$ each be a D4384: Random unsigned number such that

(i)	$X_1, \ldots, X_N$ is an D2713: Independent random collection

Let $t \in \mathbb{R}^D$ be a D4924: Euclidean real number.

Then \begin{equation} \mathbb{E} \left( e^{i t \cdot \sum_{n = 1}^N X_n} \right) = \prod_{n = 1}^N \mathbb{E} ( e^{i t \cdot X_n} ) \end{equation}

Let $X_1, \ldots, X_N \in \text{Random}(\mathbb{R}^D)$ each be a D4384: Random unsigned number such that

(i)	$X_1, \ldots, X_N$ is an D2713: Independent random collection

Then \begin{equation} \mathfrak{F} \left( \sum_{n = 1}^N X_n \right) = \prod_{n = 1}^N \mathfrak{F} \left( X_n \right) \end{equation}