Definition:Probability Measure/Definition 4

Definition

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 $

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