Chapter 9
Pointwise convergence is, perhaps, the most obvious way to de ne the convergence of functions, and it is one of the most important. Nevertheless, as the following examples illustrate, it is not as well-behaved as one might initially expect. Example 9.2. Suppose that f n: (0;1) !R is de ned by f n(x) = n nx+ 1: Then, since x6= 0, lim n!1 f n(x ...