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Writing a r.v. in set notation

  1. Jul 9, 2008 #1
    The definition I have for a random variable is
    [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??
     
  2. jcsd
  3. Jul 9, 2008 #2

    mathman

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    Gold Member

    Your espression looks right. In both cases, there is an implicit assumption that X and f(X) are real-valued.
     
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