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pushforward measure : ウィキペディア英語版
pushforward measure
In measure theory, a pushforward measure (also push forward, push-forward or image measure) is obtained by transferring ("pushing forward") a measure from one measurable space to another using a measurable function.
==Definition==
Given measurable spaces (''X''1, Σ1) and (''X''2, Σ2), a measurable mapping ''f'' : ''X''1 → ''X''2 and a measure ''μ'' : Σ1 → (), the pushforward of ''μ'' is defined to be the measure ''f''(''μ'') : Σ2 → () given by
:(f_ (\mu)) (B) = \mu \left( f^ (B) \right) \mbox B \in \Sigma_.
This definition applies ''mutatis mutandis'' for a signed or complex measure.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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