Equation 18.28.662DBAE7A20C99

\begin{equation} \sup _ K (\eta -v) = \sup _{\{ \eta \neq -\infty \} } \left(\eta - P'_{\theta ,K}[\varphi ](v)\right)=\sup _{\left\{ P'_{\theta ,K}[\varphi ](v)\neq -\infty \right\} } \left(\eta - P'_{\theta ,K}[\varphi ](v)\right). \end{equation}