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 j∈J be a projective system of Hausdorff topological spaces with maps pij : Yj → Yi. Let X be the projective limit of the system i,j∈J, i.e.
Let ε>0 be a family of probability measures on X. Assume that, for each j ∈ J, the push-forward measures ε>0 on Yj satisfy the large deviation principle with good rate function Ij : Yj → R ∪ . Then the family ε>0 satisfies the large deviation principle on X with good rate function I : X → R ∪ given by
