Let $X_1, \ldots, X_N \in \mathsf{Random}(\mathbb{R}^D)$ each be a D4383: Random euclidean real number.
Let $\mu_1, \ldots, \mu_N : \mathcal{B}(\mathbb{R}^D) \to [0, \infty]$ each be a D5241: Standard borel unsigned basic measure on $\mathbb{R}^D$ such that

(i)	\begin{equation} \mu_1(\mathbb{R}^D), \ldots, \mu_N(\mathbb{R}^D) < \infty \end{equation}
(ii)	\begin{equation} \forall \, E \in \mathcal{B}(\mathbb{R}^D) : \mathbb{P}(X_1 \in E) = \mu_1(E), \ldots, \mathbb{P}(X_N \in E) = \mu_N(E) \end{equation}

Let $B \in \mathcal{B}(\mathbb{R}^D)$ be a D5112: Standard Euclidean real Borel set.

Then \begin{equation} \mathbb{P} \Bigg( \sum_{n = 1}^N X_n \in B \Bigg) = (\mu_1 * \cdots * \mu_N)(B) \end{equation}