ThmDex – An index of mathematical definitions, results, and conjectures.
Countable subadditivity of probability measure
Formulation 1
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$
Then \begin{equation} \mathbb{P} \left( \bigcup_{n \in \mathbb{N}} E_n \right) \leq \sum_{n \in \mathbb{N}} \mathbb{P}(E_n) \end{equation}
Subresults
R4738: Finite subadditivity of probability measure
Proofs
Proof 1
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$
This result is a particular case of R3650: Countable subadditivity of unsigned basic measure. $\square$