Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space.
Let $Y, X_0, X_1, X_2, \dots \in \mathsf{Random}(\Omega \to \mathbb{R}^K)$ each be a D4383: Random euclidean real number on $P$ such that

(i)	\begin{equation} \mathbb{P} \left( \lim_{n \to \infty} X_n = Y \right) = 1 \end{equation}

Then \begin{equation} X_n \overset{p}{\longrightarrow} Y \quad \text{ as } \quad n \to \infty \end{equation}