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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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2

Borel and Radon measures

We now introduce the notion of Radon measure on images. 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 images, Theorem 1.4 provides a -algebra ...

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