8. Let f be continuous on a closed, nondegenerate interval [a, b] and set M = sup If(x)l.

xE[a,b]

127

(a) Prove that if M > 0 and p > 0, then for every € > 0 there is a nondegenerate interval I c [a, b] such that

(b) Prove that

(b) lip J~~ l lf (x)IP dx = M.