Problem 1501 (difficulty: 3/10)

Assume that \(\displaystyle f:\R\to\R\) is Lipschitz, and \(\displaystyle \forall x,y~ |f(x)-f(y)|\le K|x-y|\).

(a) Show that \(\displaystyle f\) is the integral-function of a Lebesgue-measurable \(\displaystyle g\).

(b) Show that \(\displaystyle |g|\le K\) a.e.

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