Let $X_1, \ldots, X_N \in \text{Random}(\Omega \to \mathbb{R})$ each be a D3161: Random real number such that

(i)	$X_1, \ldots, X_N$ is an D3357: Identically distributed random collection

The empirical probability distribution measure with respect to $X_1, \ldots, X_N$ is the D3650: Random probability measure \begin{equation} \Omega \times \mathcal{B}(\mathbb{R}) \to [0, 1], \quad (\omega, B) \mapsto \frac{1}{N} \sum_{n = 1}^N I_{\{ X_n \in B \}} (\omega) \end{equation}