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2003-2004 Category of density points of fat Cantor sets.
Zoltán Buczolich
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Real Anal. Exchange 29(1): 497-502 (2003-2004).


Denote by $D_{\gamma}(P)$ the set of those points where the lower Lebesgue density of $P\subset \mathbb{R}$ is bigger or equal than $\gamma.$ We show that if $\gamma>0.5$ then $D_{\gamma}(P)\cap P$ is always of first category in any nowhere dense perfect set $P$. On the other hand, there exists a fat Cantor set $Q$ which is a subset of $D_{0.5}(Q)$ while for other fat Cantor sets $P$ it is possible that $D_{+}(P)=\cup_{\gamma>0}D_{\gamma}(P)$ is of first category in $Q.$


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Zoltán Buczolich. "Category of density points of fat Cantor sets.." Real Anal. Exchange 29 (1) 497 - 502, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 9 June 2006

zbMATH: 1063.28002
MathSciNet: MR2063091

Primary: ‎28A15
Secondary: 28A75 , 54E52

Keywords: Baire category , Cantor set , density point , nowhere dense perfect set

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 1 • 2003-2004
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