= Solution
A <sigma-algebra> $\mathcal F$ on $X$ contains $\varnothing$, is closed under complements in $X$, and is closed under countable unions. A <measure> on the measurable space $(X,\mathcal F)$ is a function
$$
\mu:\mathcal F\to[0,\infty]
$$
such that $\mu(\varnothing)=0$ and, for every pairwise disjoint sequence $(A_n)$,
$$
\mu\left(\bigcup_{n=1}^{\infty}A_n\right)
=\sum_{n=1}^{\infty}\mu(A_n).
$$
A <probability measure> is a measure normalized by
$$
\boxed{\mu(X)=1.}
$$
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