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A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

W. Jurkat;  D. Nonnenmacher — 1994

Fundamenta Mathematicae

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in ℝ n , we are led to an integration process over quite general sets A ⊆ q ℝ n with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.

An axiomatic theory of non-absolutely convergent integrals in Rn

W. Jurkat;  D. Nonnenmacher — 1994

Fundamenta Mathematicae

We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.

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