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1998/1999 On the Affine Sharpness of Heartʼs Density Theorem
Marianna Csörnyei
Real Anal. Exchange 24(1): 289-294 (1998/1999).


Let $\{I_n\}_{n=1}^\infty$ be a sequence of pairwise disjoint intervals tending to 0 from the right, such that putting $I_n=(a_n,b_n)$ we have $\lim\inf {\dfrac{|I_n|}{b_n}}=0$. We prove that for every Cantor set $C$ there exists some set $X$ of positive measure, such that for a.e. $x\in X$ there exists a $c\in C$ for which $(x+cI_n)\cap X=\emptyset$ for infinitely many $n$.


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Marianna Csörnyei. "On the Affine Sharpness of Heartʼs Density Theorem." Real Anal. Exchange 24 (1) 289 - 294, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 23 March 2011

zbMATH: 0940.28006
MathSciNet: MR1691752

Primary: ‎28A15 , 28A75

Keywords: Heart's density theorem

Rights: Copyright © 1998 Michigan State University Press

Vol.24 • No. 1 • 1998/1999
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