The Divergence Theorem and Sets of Finite Perimeter

This book presents a detailed development of the divergence theorem. The framework is that of Lebesgue integration—no generalized Riemann integrals of Henstock–Kurzweil variety are involved. The first part of the book establishes the divergence theorem by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The second part introduces the sets of finite perimeter and the last part proves the general divergence theorem for bounded vector fields.