Geodesic
Variations of additive functions
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 525-555 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.
We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.
Classification : 26B05, 26B30, 28A75, 49Q15, 58C35 
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Buczolich, Zoltán; Pfeffer, Washek F. Variations of additive functions. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 525-555. http://geodesic.mathdoc.fr/item/CMJ_1997_47_3_a12/

[B] B. Bongiorno: Essential variation. Measure Theory Oberwolfach 1981, Springer Lecture Notes Math., 945, 1981, pp. 187–193. | MR

[BPS] B. Bongiorno, L. Di Piazza and V. Skvortsov: The essential variation of a function and some convergence theorems. Anal. Math. 22 (1996), no. 1, 3–12. | DOI | MR

[BPT] B. Bongiorno, W.F. Pfeffer and B.S. Thomson: A full descriptive definition of the gage integral. Canadian Math. Bull. 39 (1996), no. 4, 390–401. | DOI | MR

[BV] B. Bongiorno and P. Vetro: Su un teorema di F. Riesz. Atti Acc. Sci. Lettere e Arti Palermo (IV) 37 (1979), 3–13.

[Di] L. Di Piazza: A note on additive functions of intervals. Real Anal. Ex. 20(2) (1994–95), 815–818. | MR

[EG] L.C. Evans and R.F. Gariepy: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton, 1992. | MR

[Fe] H. Federer: Geometric Measure Theory. Springer-Verlag, New York, 1969. | MR | Zbl

[Gu] E. Giusti: Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Basel, 1984. | MR | Zbl

[P1] W.F. Pfeffer: The Gauss-Green theorem. Adv. Math. 87 (1991), 93–147. | DOI | MR | Zbl

[P3] W.F. Pfeffer: A descriptive definition of a variational integral and applications. Indiana Univ. Math. J. 40 (1991), 259–270. | DOI | MR | Zbl

[P] W.F. Pfeffer: The Riemann Approach to Integration. Cambridge Univ. Press, Cambridge, 1993. | MR | Zbl

[Sa] S. Saks: Theory of the Integral. Dover, New York, 1964. | MR

[St] E.M. Stein: Singular Integrals and Differentiability Properties of Function. Princeton Univ. Press, Princeton, 1970. | MR

[T] B. S. Thomson: Derivates of Interval Functions. Mem. Amer. Math. Soc., #452, Providence, 1991. | MR | Zbl

[V] A.I. Volpert: The spaces $BV$ and quasilinear equations. Math. USSR-SB. 2 (1967), 255–267. | MR