Abstract
Abstract The essential point leading to the proof of the theorem which follows is that the operation of integration produces more regular functions than the operation of differentiation. More precisely1 if u is a measurable and essentially bounded function on a compact interval of 1 we have no information on its derivative and do not even know if it is differentiable. On the other hand1 all of its integrals are bounded1 Lipschitz1 and differentiable almost everywhere.
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