SETS OF CLASS A1

Abstract

In this chapter we discuss the hulls of a class of sets with finite length more general than those contained in connected sets. Section 4.1 is introductory. Section 4.2 assembles some results from geometric measure theory for use in subsequent sections. Section 4.3 introduces the class A1 of sets that are the main object of study in this chapter. Section 4.4 establishes the finiteness of the area of certain one-dimensional varieties. Section 4.5 contains a version of Stokes’s theorem. Section 4.6 introduces a useful multiplicity function. Section 4.7 contains a bound on the number of global branches of a hull.