Corollary 17.13.3182AB68443E01

Corollary 17.13.31.82AB68443E01 Let $\ell \in \mathcal{R}(X,\theta ;\phi )$. Then $\sup _ X \ell _ t=\ell ^*_{\max }t$ for any $t\geq 0$.

In particular, $\ell _ t-\ell ^*_{\max }t$ is a decreasing function of $t\geq 0$.