Question: Suppose that f : R R is continuous and periodic. The modulus of continuity of f is defined by a) Show that for k

Suppose that f : R †’ R is continuous and periodic. The modulus of continuity of f is defined by
Suppose that f : R †’ R is continuous and

a) Show that

Suppose that f : R †’ R is continuous and

for k ˆˆ N.
b) Prove that

Suppose that f : R †’ R is continuous and

for k ˆˆ N.
c) Use part b) to give a different proof the Riemann-Lebesgue Lemma in the special case when f is periodic and continuous.

o(f, ) = lft + h)-f(t)I. sup his ST a and l((s.)

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