ABSTRACT

In this chapter, we shall deal with convergence of sequence of functions. Let X be a nonempty set, not necessarily a subset of R. Let fn : X → R be a function, n ∈ N. We then say (fn) is a sequence of functions on X. Example 7.0.1. Let X = [0, 1]. Define fn(x) := x/n, x ∈ [0, 1]. Then (fn) is a sequence of functions on [0, 1].