The fundamental theorem of geometric calculus via a generalized Riemann integral

Abstract

Using recent advances in integration theory, we give a proof of the fundamental theorem of geometric calculus. We assume only that the tangential derivative ${\nabla }_{V}F$ exists and is Lebesgue integrable. We also give sufficient conditions that ${\nabla }_{V}F$ exists.

To appear in Advances in Applied Clifford Algebras