# Non-absolutely convergent integrals in metric spaces

created by maly on 04 Jul 2011

[BibTeX]

Preprint

Inserted: 4 jul 2011

Year: 2011

Abstract:

The rich structure of the real line or of the Euclidean space allows to assign a kind of integral to some highly oscillating functions which are not absolutely (Lebesgue) integrable; such integrals have been introduced by Denjoy, Perron, Luzin, Henstock, Kurzweil and others. We show that already the structure on metric space is enough to establish a natural concept of a nonabsolutely convergent integral. We integrate functions with respect to distributions'', which (in this metric space setting) are dual objects to Lipschitz test functions. We apply the new integral in the Ambrosio-Kirchheim theory of metric currents in connection with the Stokes formula.