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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 n , we are led to an integration process over quite general sets A q 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.

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