Definition:Probability Measure/Definition 4

From ProofWiki
Jump to navigation Jump to search


Let $\EE$ be an experiment.

Let $\Omega$ be the sample space on $\EE$.

Let $\Sigma$ be the event space of $\EE$.

A probability measure on $\EE$ is an additive function $\Pr: \Sigma \to \R$ which fulfils the following axioms:

\((1)\)   $:$     \(\ds \forall A, B \in \Sigma: A \cap B = \O:\)    \(\ds \map \Pr {A \cup B} \)   \(\ds = \)   \(\ds \map \Pr A + \map \Pr B \)      
\((2)\)   $:$      \(\ds \map \Pr \Omega \)   \(\ds = \)   \(\ds 1 \)      

Also see