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Luzin's theorem for charges

Authors: Eric J. Howard and Washek F. Pfeffer
Journal: Proc. Amer. Math. Soc. 132 (2004), 857-863
MSC (2000): Primary 28A15; Secondary 26A45
Published electronically: 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 [Enhancements On Off] (What's this?)

  • 1. Lawrence C. Evans and Ronald F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1158660
  • 2. N. Luzin, Sur la notion de l'intégrale, Annali Mat. Pura e Appl. (3), 26 (1917), 77-129.
  • 3. Washek F. Pfeffer, Derivation and integration, Cambridge Tracts in Mathematics, vol. 140, Cambridge University Press, Cambridge, 2001. MR 1816996
  • 4. Stanisław Saks, Theory of the integral, Second revised edition. English translation by L. C. Young. With two additional notes by Stefan Banach, Dover Publications, Inc., New York, 1964. MR 0167578

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Additional Information

Eric J. Howard
Affiliation: Division of Mathematics and Computer Science, Truman State University, Kirksville, Missouri 63501

Washek F. Pfeffer
Affiliation: Department of Mathematics, University of California, Davis, California 95616

Keywords: BV set, charge, derivative
Received by editor(s): November 13, 2002
Published electronically: October 8, 2003
Communicated by: David Preiss
Article copyright: © Copyright 2003 American Mathematical Society