ABSTRACT
This chapter is mostly a review of standard measure theory, with particular attention paid to Radon measures on Rn.
Sections 1.1 through 1.4 are a rapid recounting of abstract measure theory. In Section 1.5 we establish Vitali’s and Besicovitch’s Covering Theorems, the latter being the key for the Lebesgue-Besicovitch Differentiation Theorem for Radon measures in Sections 1.6 and 1.7. Section 1.8 provides a vector-valued version of Riesz’s Representation Theorem. In Section 1.9 we study weak compactness for sequences of measures and functions.
