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In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder set measures are in general not measures (and in particular need not be countably additive but only finitely additive), but can be used to define measures, such as classical Wiener measure on the set of continuous paths starting at the origin in Euclidean space. ==Definition== Let ''E'' be a separable, real, topological vector space. Let denote the collection of all surjective, continuous linear maps ''T'' : ''E'' → ''F''''T'' defined on ''E'' whose image is some finite-dimensional real vector space ''F''''T'': : A cylinder set measure on ''E'' is a collection of probability measures : where ''μ''''T'' is a probability measure on ''F''''T''. These measures are required to satisfy the following consistency condition: if ''π''''ST'' : ''F''''S'' → ''F''''T'' is a surjective projection, then the push forward of the measure is as follows: : 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「Cylinder set measure」の詳細全文を読む スポンサード リンク
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