= Complete sufficient statistic
{title2=$\mathbb E_\theta g(T)=0\ \forall\theta\Longrightarrow g(T)=0\text{ a.s.}$}
A <sufficient statistic> is complete when every integrable function of it with <expectation> zero for every parameter is almost surely zero for every parameter. Full regular one-parameter <exponential families> with natural parameter ranging over an open interval provide a standard completeness result. Completeness makes an unbiased function of a <sufficient statistic> unique, giving the <Lehmann–Scheffé theorem>.
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