Luzin’s theorem for charges
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- by Eric J. Howard and Washek F. Pfeffer PDF
- Proc. Amer. Math. Soc. 132 (2004), 857-863 Request permission
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
- 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
- N. Luzin, Sur la notion de l’intégrale, Annali Mat. Pura e Appl. (3), 26 (1917), 77–129.
- Washek F. Pfeffer, Derivation and integration, Cambridge Tracts in Mathematics, vol. 140, Cambridge University Press, Cambridge, 2001. MR 1816996, DOI 10.1017/CBO9780511574764
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
Additional Information
- Eric J. Howard
- Affiliation: Division of Mathematics and Computer Science, Truman State University, Kirksville, Missouri 63501
- Email: ehoward@truman.edu
- Washek F. Pfeffer
- Affiliation: Department of Mathematics, University of California, Davis, California 95616
- MR Author ID: 138980
- Email: wfpfeffer@ucdavis.edu
- Received by editor(s): November 13, 2002
- Published electronically: October 8, 2003
- Communicated by: David Preiss
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 857-863
- MSC (2000): Primary 28A15; Secondary 26A45
- DOI: https://doi.org/10.1090/S0002-9939-03-07276-9
- MathSciNet review: 2019966