ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4318 on D1158: Measure space
Subresult of R2086: Finite inclusion-exclusion principle for unsigned basic measure

Inclusion-exclusion principle for unsigned basic measure of binary union

Formulation 0

Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
Let $E, F \in \mathcal{F}$ each be a D1109: Measurable set in $M$ such that

(i)	\begin{equation} \mu(E), \mu(F) < \infty \end{equation}

Then \begin{equation} \mu(E \cup F) = \mu(E) + \mu(F) - \mu(E \cap F) \end{equation}

Subresults

▶	R4445: Inclusion-exclusion principle for probability of binary union

Proofs

Proof 0

Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
Let $E, F \in \mathcal{F}$ each be a D1109: Measurable set in $M$ such that

(i)	\begin{equation} \mu(E), \mu(F) < \infty \end{equation}