Open Access
2009/2010 A Generalization of Steinhaus' Theorem and Some Nonmeasurable Sets
Robert Rałowski, Przemysław Szczepaniak, Szymon Żeberski
Real Anal. Exchange 35(2): 403-412 (2009/2010).


We generalize a classical Steinhaus theorem replacing addition by any two variable function which is differentiable. We deal with category and measure case. Measure case was done before in papers [3], [9]. We give a proof which can be easily generalized to category case. We also obtain a variety of examples of nonmeasurable sets which have interesting algebraic properties.


Download Citation

Robert Rałowski. Przemysław Szczepaniak. Szymon Żeberski. "A Generalization of Steinhaus' Theorem and Some Nonmeasurable Sets." Real Anal. Exchange 35 (2) 403 - 412, 2009/2010.


Published: 2009/2010
First available in Project Euclid: 22 September 2010

zbMATH: 1225.03060
MathSciNet: MR2683606

Primary: 03E35 , 03E75
Secondary: 28A99

Keywords: meager set , nonmeasurable set , null set , real line

Rights: Copyright © 2009 Michigan State University Press

Vol.35 • No. 2 • 2009/2010
Back to Top