= Expected utility representation on a finite measurable space
{title2=$U_0(\lambda)=\int U\,d\lambda$}
Set $U(x)=U_0(\delta_x)$. On a finite measurable space, points in the same <atom of a sigma-algebra> give the same <Dirac measure>, so $U$ is a <measurable function> and constant on atoms. Every <probability measure> is a finite mixture of representative <Dirac measures> with its atom masses as weights. Affineness then proves the expected-utility representation, even when the <sigma-algebra> is smaller than the <power set>.
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