Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Luzin's theorem for charges

Author(s): Eric J. Howard; Washek F. Pfeffer
Journal: Proc. Amer. Math. Soc. 132 (2004), 857-863.
MSC (2000): Primary 28A15; Secondary 26A45
Posted: October 8, 2003
MathSciNet review: 2019966
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Abstract | References | Similar articles | Additional information

Abstract: A charge in the Euclidean space $\mathbb{R} ^m$ is an additive function defined on the family of all bounded BV sets equipped with a suitable topology. We define derivatives of charges and show that each measurable function defined on $\mathbb{R} ^m$ is equal almost everywhere to the derivative of a charge.

References:

1.: L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992. MR 93f:28001
2.: N. Luzin, Sur la notion de l'intégrale, Annali Mat. Pura e Appl. (3), 26 (1917), 77-129.
3.: W. F. Pfeffer, Derivation and Integration, Cambridge Tracts in Mathematics, No. 140, Cambridge University Press, Cambridge, 2001. MR 2001m:26018
4.: S. Saks, Theory of the Integral, Dover Publications, New York, 1964. MR 29:4850

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