(i) | $F \subseteq X$ is a D78: Subset of $X$ |

**counting measure**on $M$ with respect to $F$ is the D4361: Unsigned basic function \begin{equation} \mathcal{F} \to [0, \infty], \quad E \mapsto |E \cap F| \end{equation}

Definition D1225

Counting measure

Formulation 0

Let $M = (X, \mathcal{F})$ be a D1108: Measurable space such that

The **counting measure** on $M$ with respect to $F$ is the D4361: Unsigned basic function
\begin{equation}
\mathcal{F} \to [0, \infty], \quad
E \mapsto |E \cap F|
\end{equation}

(i) | $F \subseteq X$ is a D78: Subset of $X$ |

Children

▶ | Point measure |

▶ | Standard counting measure |