Non-absolutely convergent integrals with respect to distributions

Abstrakt

We define an integral of a function with respect to a distribution. In case that the underlying distribution is just the Lebesgue measure, the definition leads to a new non-absolutely convergent integral which is wider than the Denjoy-Perron integral.

We present a version of the Gauss-Green theorem where the new integral is used for both interior and boundary terms. As a by-product, we characterize the predual Sobolev space W (1,1).

Klíčová slova

• Non-absolutely convergent integrals
• Distributions
• Gauss-Green theorem