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Definition 19.6.5F0D4BAA63D8A

Definition 19.6.5.F0D4BAA63D8A A test function on $\Delta $ is a function $G\colon \Delta \rightarrow [-\infty ,\infty )$ such that

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    $G$ is concave,

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    $G$ is finite on $\operatorname{Int}\Delta $, and

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    $G$ is upper semicontinuous.

A test function $G$ is bounded if $G$ is bounded from below.

A test function $G$ has finite energy if

6B100556700A 19.6.6
\begin{equation} \mathbf{E}(G)\coloneqq n!\int _{\Delta } G\, \mathrm{d}\lambda >-\infty . \end{equation}
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