Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 26K / a / 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 functionsuch that $\mu (\varnothing )=0$ and, for every pairwise disjoint sequence $(A_n)$,A probability measure is a measure normalized by