Pfeffer, Washek F. An integral in geometric measure theory. (English) Zbl 0797.26007 Atti Semin. Mat. Fis. Univ. Modena 41, No. 1, 59-76 (1993). 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. Reviewer: J.Mawhin (Louvain-La-Neuve) MSC: 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) Keywords:BV sets; multidimensional conditionally convergent integrals; Gauss-Green theorem; noncontinuously differentiable vector fields PDFBibTeX XMLCite \textit{W. F. Pfeffer}, Atti Semin. Mat. Fis. Univ. Modena 41, No. 1, 59--76 (1993; Zbl 0797.26007)