= Solution
A <measure space> consists of a set $\Omega$, a sigma-algebra $\mathcal A$ of subsets, and a countably additive map $\mu:\mathcal A\to[0,\infty]$ with $\mu(\varnothing)=0$. A sigma-algebra contains $\Omega$ and is closed under complements and <countable unions>. <Countable additivity> means $\mu(\bigcup_nA_n)=\sum_n\mu(A_n)$ for pairwise disjoint <measurable sets>. Such sets are called <measurable>; a real function is <measurable> when the inverse image of every <Borel set> belongs to $\mathcal A$.
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