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Fubini's theorem

  1. Feb 22, 2014 #1
    I remember a teacher speaking that the fubini's theorem is valid under certain conditions. Implying that not is valid under others. I didn't understood exactly what this teacher was speaking, but the doubt remains still today. We know that ##\frac{\partial^2 f}{\partial y \partial x}## is always equal to ##\frac{\partial^2 f}{\partial x \partial y}##, unless that proofs the contrary. The same way, ##\int \int f\;dx dy## is unconditionally equals to ##\int \int f\;dy dx##?
     
  2. jcsd
  3. Feb 22, 2014 #2

    lurflurf

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    Neither of those are true in general. A commonly given sufficient condition is that limits can be interchanged if the convergence is uniform. That being many times the conditions are met.
     
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