## ABSTRACT

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 an

DYADIC FIGURES: Preliminaries. Divergence Theorem for Dyadic Figures. Removable Singularities. SETS OF FINITE PERIMETER: Perimeter. BV Functions. Locally BV Sets. THE DIVERGENCE THEOREM: Bounded Vector Fields. Unbounded Vector Fields. Mean Divergence. Charges. The Divergence Equation.