Talk:Pushforward measure

Latest comment: 2 years ago by AVM2019 in topic "Random variables are pushforward measures"


Thanks

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Thanks for elaborating this page. I have relinked to here as much as possible. Now I will take it off my watch list. Good luck! Geometry guy 00:17, 12 February 2007 (UTC)Reply

Attention needed to the definition/examples? [Resolved]

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The first example seems to state that the measure of an arc   of the circle is equal to the measure of   on the real line, where   is the wrap-around function. But   has measure  .

Should the correct definition define  ? Am I missing something?

69.81.71.60 (talk) 11:54, 28 June 2017 (UTC)Reply

No, why? It is written "Let λ also denote the restriction of Lebesgue measure to the interval [0, 2π)". Also f is defined on [0, 2π). Not infinity. Boris Tsirelson (talk) 18:47, 28 June 2017 (UTC)Reply
I see now. Thank you! Norbornene (talk) 13:29, 9 July 2017 (UTC)Reply

"Random variables are pushforward measures"

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As far as I can see, the following statement is false:

Random variables are pushforward measures

A r.v. defines a pushforward measure, but there is not one-to-one identification. For example, i.i.d r.v.'s   define the same pushforward measure  , although they are clearly distinct mappings from the probability space   to a measurable space  . AVM2019 (talk) 12:50, 19 May 2022 (UTC)Reply