Definition:Rate Function

Definition

Let $X$ be a topological space.

Let $\overline \R_\ge$ be the positive extended real number line.

Let $I : X \to \overline \R_\ge$ be a function.

Then $I$ is a rate function if and only if $I$ is lower semicontinuous.

Sources

• 1998: Amir Dembo and Ofer Zeitouni: Large Deviations Techniques and Applications (2nd ed.): $1.2$ The Large Deviation Principle