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m How is it untrue? Please discus on the article's talk page. (HG) (3.4.9) |
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==Definition==
Let <math>(\Omega, \mathcal F, P)</math> be a [[probability space]], and let <math>T:\Omega\rightarrow E</math> be a [[random variable]], defined as a [[Borel measure|Borel-]][[measurable function]] from <math>\Omega</math> to its [[Probability space#Random variables|state space]] <math>(E, \mathcal E)
One should think of <math>T</math> as a way to "disintegrate" the sample space <math>\Omega</math> into <math>\{ T^{-1}(x) \}_{x \in E}</math>.
Using the [[disintegration theorem]] from the measure theory, it allows us to "disintegrate" the measure <math>P</math> into a collection of measures,
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