The definition I have for a random variable is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]X=\lbrace \omega \in \Omega \vert X(\omega) \in B \rbrace \in F[/tex] where F is a sigma algebra and B is a Borel subset of R.

Using function composition, how would one write a similar set notation definition for f(X), where f is a Borel measurable function?

[tex]f(X)=\lbrace \omega \in \Omega \vert f(X(\omega)) \in B \rbrace \in \sigma(X)[/tex] where [tex]\sigma(X)[/tex] is a sigma algebra and B is a Borel subset of R??

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# Writing a r.v. in set notation

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