Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
The standard counting measure on $M$ is the D4361: Unsigned basic function
\begin{equation}
\mathcal{F} \to [0, \infty], \quad
E \mapsto |E|
\end{equation}
▶ | D5637: Standard natural number counting measure |