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  3. 4. define the width of a rectangle as the longest

4. Define the width of a rectangle as the longest length of its sides. Given a...

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Advance Math

4. Define the width of a rectangle as the longest length ofits sides. Given a closed
rectangle A in Rn and a partition P of A, define the mesh of Pas the maximum
width of its subrectangles. Prove that a bounded function f :A ? R is integrable
on A if and only if, for every > 0, there is a ? > 0such that U(f, P) ? L(f, P) <
for every partition P of mesh < ?.

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