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An integral in geometric measure theory. (English) Zbl 0797.26007

This paper describes some recent work of the author on multidimensional conditionally convergent integrals related to the Gauss-Green theorem. The obtained integral is defined on the family BV of all bounded measurable subsets of the \(n\)-dimensional Euclidean space whose perimeter in De Giorgi sense is finite. It is coordinate free and provides a Gauss- Green theorem for noncontinuously differentiable vector fields with large sets of singularities.
The paper is aimed for nonspecialists and the author may be credited for a very clear exposition.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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