Thread: Proving limits of integrals

Problem: Define the rectangles

X and

Also define R = [0,1] X [0,1]. Suppose f is a bounded function on R and that f is integrable over each .
(a) Prove that f is integrable over R.
(b) Define the integrals

and

Prove that
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Can I get a hint on how to start (b)?

Using the fact that is bounded, show that the area of tends to .

Originally Posted by girdav

Using the fact that is bounded, show that the area of tends to .

I was told that this might not work because the area of might not be of zero content.