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

Volume 146 / 1994

W. Jurkat, D. Nonnenmacher Fundamenta Mathematicae 146 (1994), 69-84 DOI: 10.4064/fm-146-1-69-84

Abstract

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.

Authors

  • W. Jurkat
  • D. Nonnenmacher

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