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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. ==Statement of the theorem== Let (''Y''''j'')''j''∈''J'' be a projective system of Hausdorff topological spaces with maps ''p''''ij'' : ''Y''''j'' → ''Y''''i''. Let ''X'' be the projective limit (also known as the inverse limit) of the system (''Y''''j'', ''p''''ij'')''i'',''j''∈''J'', i.e. : Let (''μ''''ε'')''ε''>0 be a family of probability measures on ''X''. Assume that, for each ''j'' ∈ ''J'', the push-forward measures (''p''''j''∗''μ''''ε'')''ε''>0 on ''Y''''j'' satisfy the large deviation principle with good rate function ''I''''j'' : ''Y''''j'' → R ∪ . Then the family (''μ''''ε'')''ε''>0 satisfies the large deviation principle on ''X'' with good rate function ''I'' : ''X'' → R ∪ given by : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dawson–Gärtner theorem」の詳細全文を読む スポンサード リンク
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