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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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3

Hausdorff measures

Hausdorff measures provide an important source of examples of Radon measures. For this reason, before further developing the theory of Radon measures, in this chapter we take a closer look at Hausdorff measures. In Section 3.1 we introduce and motivate the notion of Hausdorff dimension. In Section 3.2 we relate images1 to the classical notion of length of a curve. Finally, in Section 3.3 we show equivalence of the Lebesgue measure and imagesn on n.

3.1 Hausdorff measures and the notion of dimension

We begin our discussion by introducing ...

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