ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4739 on D198: Probability measure
Binary subadditivity of probability measure
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $E, F \in \mathcal{F}$ are each an D1716: Event in $P$
Then \begin{equation} \mathbb{P} \left( E \cup F \right) \leq \mathbb{P}(E) + \mathbb{P}(F) \end{equation}
Proofs
Proof 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $E, F \in \mathcal{F}$ are each an D1716: Event in $P$
This result is a particular case of R4738: Finite subadditivity of probability measure. $\square$