Probability axioms
The facts that the probability
of event is a non-negative real number,
\[ \forall A, \> \Pr(A) \geq 0 \]
of sample space is the unit,
\[ \Pr(\Omega) = 1 \]
of mutually exclusive events is
\[\Pr(A_1 \cup A_2 \cup \ldots) = \Pr(A_1) + \Pr(A_2) + \cdots\]
or equivalently
\[\Pr( \bigcup_{i = 1}^{\infty} E_i ) = \sum_{i = 1}^{\infty} \Pr(E_i).\]