Dawson–Gärtner theorem

In mathematics, the Dawson–Gärtner theorem is a result in large deviations theory.

Heuristically speaking, the Dawson–Gärtner theorem allows one to transport a large deviation principle on a “smaller” topological space to a “larger” one.

Let X be the projective limit (also known as the inverse limit) of the system (Yj, pij)i,j∈J, i.e. Let (με)ε>0 be a family of probability measures on X.

Assume that, for each j ∈ J, the push-forward measures (pj∗με)ε>0 on Yj satisfy the large deviation principle with good rate function Ij : Yj → R ∪ {+∞}.

Then the family (με)ε>0 satisfies the large deviation principle on X with good rate function I : X → R ∪ {+∞} given by