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1999/2000 Symmetrically Continuous Functions on Various Subsets of the Real Line
Marcin Szyszkowski
Real Anal. Exchange 25(2): 547-564 (1999/2000).


We define symmetric continuity for functions defined on arbitrary subsets of $\mathbb{R}$. The main result is that when a symmetrically continuous function is defined on a measurable set (a set with the Baire property), then it is continuous almost everywhere (on a residual set, respectively). This generalizes the known result for functions defined on the whole real line.


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Marcin Szyszkowski. "Symmetrically Continuous Functions on Various Subsets of the Real Line." Real Anal. Exchange 25 (2) 547 - 564, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1016.26003
MathSciNet: MR1778510

Primary: 26A15

Keywords: Baire property , measurability , symmetrically continuous

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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