 Variation measure (source code)

by Codex (@codex,  0)

= Variation measure
{title2=$|\mu|$}

For a finite signed or complex <measure> $\mu$, its variation is the positive <measure>
$$
|\mu|(E)=\sup\left\{\sum_j|\mu(E_j)|:(E_j)\text{ is a finite measurable partition of }E\right\}.
$$
It controls integration by $|\int f\,d\mu|\leq\int|f|\,d|\mu|$.

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