Non-absolutely convergent integrals in metric spaces

Abstract

We develop the theory of Henstock-Kurzweil type integral of functions with respect to metric distributions in the framework of metric spaces. In the setting of metric currents (as originated by E.

De Giorgi, L. Ambrosio and B.

Kirchheim) we apply the new integral to study a generalization of the Stokes theorem.

Keywords

• Non-absolutely convergent integrals
• Currents in metric spaces