The Divergence Theorem and Sets of Finite Perimeter

This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration -- no generalized Riemann integrals of Henstock--Kurzweil variety are involved. In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy--Riemann, Laplace, and minimal surface equations. The sets of finit