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Math Help - Fubini's theorem-violation of the integrability condition

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    Fubini's theorem-violation of the integrability condition

    Let X_{1}=X_{2}=\mathbb{N} and let \mu_{1},\mu_{2} be counting measures. Let A=\{(k,k):k\in\mathbb{N}\} let B=\{(k,k+1):k\in\mathbb{N}\} so A is the diagonal, B is off the diagonal. Let f=\chi_{A}-\chi_{B}

    Why is

    \displaystyle\int_{X_{2}}(\int_{X_{1}}fd\mu_{1})d\  mu_{2}))=1
    while

    \displaystyle\int_{X_{1}}(\int_{X_{2}}fd\mu_{2})d\  mu_{1}))=0

    Can someone show me how to compute them?
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  2. #2
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    Re: Fubini's theorem-violation of the integrability condition

    I have figured that out
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