= Solution
The <probability measure> $\mathbb P$ maps the <sigma-algebra> $\mathcal F$ of events into $[0,1]$. Its <probability axioms> are nonnegativity, normalization $\mathbb P(\Omega)=1$, and <countable additivity>: for every pairwise disjoint sequence of events $A_1,A_2,\ldots$,
$$
\mathbb P\left(\bigcup_{n=1}^\infty A_n\right)=\sum_{n=1}^\infty\mathbb P(A_n).
$$
The <sample space> is $\Omega$, and $\mathcal F$ specifies which subsets are events. Requiring <countable additivity>, rather than only its finite version, is part of the <probability space> definition.
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