Good rate function
= Good rate function
{title2=$I$}
A <rate function> is a <lower semicontinuous> map $I:E\to[0,\infty]$. It is good if every sublevel set $\{I\leq M\}$ is a <compact set>. This property controls escapes to infinity and makes the minimizations in the <contraction principle for large deviations> attain their finite infima. On $\mathbb R^d$, a <lower semicontinuous> <rate function> tending to infinity with the norm is good.