Let $X \in \mathsf{Random}(\mathbb{R}^N)$ be a D4383: Random euclidean real number such that

(i)	\begin{equation} \exists \, a \in \mathbb{R}^N : \mathbb{P}(X = a) = 1 \end{equation}

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

Since $X$ takes value $a$ with probability one, then the random variable $e^{i t \cdot X}$ takes value $e^{i t \cdot a}$ with probability one. Thus, applying R1814: Expectation of discrete random euclidean real number, we have \begin{equation} \mathbb{E}(e^{i t \cdot X}) = e^{i t \cdot a} \mathbb{P}(X = a) = e^{i t \cdot a} \end{equation} $\square$