ABSTRACT
There are many ways a sequence of functions in a measure space can converge. In this chapter, the author explores some of them and the relationships between them. In some cases, when a sequence of functions converges in one way, it is possible to prove that there is at least one subsequence that converges in a different manner. A famous theorem tells us how the convergence can be phrased “almost” like uniform convergence. This is Egoroff’s Theorem. The important Vitali’s theorem is one that gives us more technical tools to characterize p-norm convergence for a sequence of functions.
