Borel and Radon measures
We now introduce the notion of Radon measure on . Section 2.1 introduces the related notion of Borel measure, with a useful characterization result due to Carathéodory. In Section 2.2 we define Borel regular measures, while in Section 2.3 we prove two fundamental approximation theorems. The definition of Radon measure appears in Section 2.4, with a brief discussion about basic examples, operations, and useful facts.
2.1 Borel measures and Carathéodory's criterion
Given an outer measure , Theorem 1.4 provides a -algebra ...