Let E c1, c2, and let F be continuous on a, b and F Ecirc sup1 (x) f(x) for x a, b E and f(ck) 0 We want to show that f R a, b and that equation (5) holds (a) Given Icirc micro 0 and t a, b E, let Icirc acute Icirc micro (t) be defined as in the proof of 10 1 9 Choose Icirc acute Icirc micro (ck) 0...

a This is possible since F is continuous at ck b Since fc k ...

Let E := {c1, c2, . . .} and let F be continuous on [a, b] and

Question:

Let E := {c1, c2, . . .} and let F be continuous on [a, b] and FÊ¹(x) = f(x) for x ˆˆ [a, b]E and f(ck) := 0. We want to show that f ˆˆ R*[a, b] and that equation (5) holds.
(a) Given Îµ > 0 and t ˆˆ [a, b]E, let Î´Îµ(t) be defined as in the proof of 10.1.9. Choose Î´Îµ(ck) > > 0 such that if |z - ck|