Open Access
2010/2011 There are Measurable Hamel Functions
Rafał Filipów, Andrzej Nowik, Piotr Szuca
Real Anal. Exchange 36(1): 223-230 (2010/2011).


We say that a function $f:\mathbb{R}\to \mathbb{R}$ is a {\it Hamel function} if $f$, considered as a subset of $\mathbb{R}^2$, is a Hamel basis of $\mathbb{R}^2$. We show that there is a Marczewski measurable Hamel function. Additionally, we show that there is a Hamel function which is both Lebesgue measurable and with the Baire property.


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Rafał Filipów. Andrzej Nowik. Piotr Szuca. "There are Measurable Hamel Functions." Real Anal. Exchange 36 (1) 223 - 230, 2010/2011.


Published: 2010/2011
First available in Project Euclid: 14 March 2011

zbMATH: 1260.28002
MathSciNet: MR3016414

Primary: 15A03%Vectorspaces,lineardependence,rank
Secondary: 26A21%Classificationofrealfunctions;Baireclassificationofsetsandfunctions , 28A05 , ‎54C30

Keywords: Borel set , closed Lebesgue null set , function with the Baire property , Hamel basis , Hamel function , Lebesgue measurable function , Marczewski measurable function , porous set

Rights: Copyright © 2010 Michigan State University Press

Vol.36 • No. 1 • 2010/2011
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