= Log-density domination in an exponential family
On a bounded parameter set, $\log f_\theta(x)=\theta x-K(\theta)+\log f_0(x)$ has an <integrable envelope of a function class> whenever $K$ is bounded and $|X|+|\log f_0(X)|$ is integrable under the sampling law. A <compact> subset of the interior natural-parameter domain bounds the <cumulant function of an exponential family> and provides moments under model sampling; log-base-density <integrability> is an additional condition.
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