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In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are “the same” from the point of view of large deviations theory. ==Definition== Let (''M'', ''d'') be a metric space and consider two one-parameter families of probability measures on ''M'', say (''μ''''ε'')''ε''>0 and (''ν''''ε'')''ε''>0. These two families are said to be exponentially equivalent if there exist * a one-parameter family of probability spaces ((Ω, Σ''ε'', P''ε''))''ε>0, * two families of ''M''-valued random variables (''Y''''ε'')''ε''>0 and (''Z''''ε'')''ε''>0, such that * for each ''ε'' > 0, the P''ε''-law (i.e. the push-forward measure) of ''Y''''ε'' is ''μ''''ε'', and the P''ε''-law of ''Z''''ε'' is ''ν''''ε'', * for each ''δ'' > 0, “''Y''''ε'' and ''Z''''ε'' are further than ''δ'' apart” is a Σ''ε''-measurable event, i.e. :: * for each ''δ'' > 0, :: The two families of random variables (''Y''''ε'')''ε''>0 and (''Z''''ε'')''ε''>0 are also said to be exponentially equivalent. 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「Exponentially equivalent measures」の詳細全文を読む スポンサード リンク
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