All of these integrals are riemann not lebesgue integrals.

Problem statement:

Let $f$ and $g$ be real-valued functions on a subset $A$ of $E^n$. Show that if $\int_{A} f$ and $\int_{A} g$ exist then $\int_{A} fg$ exists.

I have already proven that if $f$ and $g$ are integrable on a closed interval $I$ of $E^n$ then so is $fg$ so maybe we can use this fact?

  • $\begingroup$ And what is $E^n$? $\endgroup$ – Paul Sinclair Dec 6 '15 at 22:15
  • $\begingroup$ $E^n$ is a metric space. $\endgroup$ – Chair Dec 7 '15 at 13:44
  • $\begingroup$ How are you defining integration on an arbitrary metric space? What do you mean by an "Interval" in an arbitrary metric space? Or is there more to $E^n$ than just "metric space"? $\endgroup$ – Paul Sinclair Dec 7 '15 at 21:23

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