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Math Help - an extended real-valued function

  1. #1
    Junior Member
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    an extended real-valued function

    Let
    f : X ->[- infinity, infinity] be an extended real-valued function defined on a

    measure space
    ( X, F, m) . Prove that {x : f (x ) > -infinity}
    is in segma-algebra F ,and {x: - infinity< f(x)< infinity}
    is in segma-algebra F

    how can I apply the definition of an extended real-valued function to prove this, any help would be appraciated.
    Thanks,

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  2. #2
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    any idea how to solve it would be appreciated
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  3. #3
    Senior Member Tinyboss's Avatar
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    It seems like you're missing something from your problem statement, because unless F=P(X), we can choose some subset A of X such that A is not in F, and define f by

    f(x)=\begin{cases}0&x\in A\\-\infty&x\notin A.\end{cases}

    Maybe f is supposed to be measurable?
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