ABSTRACT
In this chapter, the authors begin by formally defining the most obvious notion of convergence for a series of functions. The most obvious notion of convergence for a series of functions is pointwise convergence. However, this turns out to be less important than another sort of convergence, uniform convergence. The authors define the Fourier series of a periodic function, it is natural to ask when the Fourier series of a function converges to the function. The problem of convergence of Fourier series is a difficult one and is still a subject of research in mathematics. The authors investigate some properties of uniform convergence. They deal primarily with functions defined on subsets of R, leaving various generalizations as exercises.
