Geodesic
A full descriptive definition of the BV-integral
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 461-469.

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We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.
Classification : 26A39, 26B30, 28A75
Keywords: Perimeter; partition; gage; absolute continuity 
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Bongiorno, B.; Di Piazza, L.; Pfeffer, W. F. A full descriptive definition of the BV-integral. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 461-469. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a6/