Let f be as in Exercise 19 and let m(x) := (-1)k for x [ak, bk](k

Question:

Let f be as in Exercise 19 and let m(x) := (-1)k for x ∈ [ak, bk](k ∈ N), and m(x) := 0 elsewhere in [0, 1]. Show that m ∙ f = |m ∙ f|. Use Exercise 7.2.11 to show that the bounded functions m and |m| belong to R[0, 1]. Conclude that the product of a function in R*[0, 1] and a bounded function in R[0, 1] may not belong to R*[0, 1].