Open Access
2003-2004 Symmetric derivatives on subsets of the real line and monotonicity.
Marcin Szyszkowski
Author Affiliations +
Real Anal. Exchange 29(2): 799-804 (2003-2004).


We define and investigate the symmetric derivative for functions defined on a subset of the real line. We give an example of a continuous function with a positive symmetric derivative everywhere which is not monotonic. When the domain is measurable or has the Baire property, then a positive symmetric derivative does imply monotonicity on a big set.


Download Citation

Marcin Szyszkowski. "Symmetric derivatives on subsets of the real line and monotonicity.." Real Anal. Exchange 29 (2) 799 - 804, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1077.26004
MathSciNet: MR2083814

Primary: 26A15

Keywords: Baire property , measurability , symmetric continuity

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
Back to Top