(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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

▾ Point-mass measure

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

▾ Point-mass 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 $X$ |

Child definitions