×

Non-absolutely convergent integrals in metric spaces. (English) Zbl 1264.26015

Summary: We develop a 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 Stoke’s theorem.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
26A39 Denjoy and Perron integrals, other special integrals
28D20 Entropy and other invariants
PDFBibTeX XMLCite
Full Text: DOI