1 Show that the product of two regulated functions is regulated. 2. A function is regulated if it is the limit of a sequence of step functions. 3. I let f,g be regulated and let a_n, b_n tend to f, g respectivley. I can show that for any x, a_n (x) . b_n (x) tends to f(x).g(x) (i.e. pointwise convergence). Is this sufficient or do I need to show uniform convergence? If so how do I go about it?