ABSTRACT
In this chapter we discuss Hausdorff measures, a generalization of Lebesgue measure. Hausdorff measure is defined in terms of coverings of sets which have small diameters and the quantity which is important is the diameters of the sets. The concept will be used to present a simple and unified treatment of surface measure in later chapters. To study Hausdorff measures, we will use many ideas from earlier chapters, in particular the following lemma found at the beginning of Chapter 14.
