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Math Help - measurable and integrable of product space

  1. #1
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    measurable and integrable of product space

    Let f : (0,1) >R be measurable( w.r.t. Lebesgue measure) function in L1((0,1)). Define the function g on (0,1) (0,1) by

    g(x,y)=f(x)/x if 0<y<x<1
    g(x,y)=0 if 0<x≤y<1

    Prove:
    1) g is measurable function (w.r.t. Lebesgue measure in the prodcut (0,1) (0,1)

    2)g is integrable in (0,1) (0,1)
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  2. #2
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    Re: measurable and integrable of product space

    What are you looking for? For #1, use the definition of a measurable function. For #2, use the definition of an integrable function.
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