4. Define the width of a rectangle as the longest length of
its sides. Given a closed
rectangle A in Rn and a partition P of A, define the mesh of P
as 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 δ > 0
such that U(f, P) − L(f, P) <
for every partition P of...