Open Access
2001/2002 Measure Zero Sets with Non-Measurable Sum
Krzysztof Ciesielski, Hajrudin Fejzić, Chris Freiling
Real Anal. Exchange 27(2): 783-794 (2001/2002).


For any $C\subseteq \mathbb{R}$ there is a subset $A\subseteq C$ such that $A+A$ has inner measure zero and outer measure the same as $C+C$. Also, there is a subset $A$ of the Cantor middle third set such that $A+A$ is Bernstein in $[0,2]$. On the other hand there is a perfect set $C$ such that $C+C$ is an interval $I$ and there is no subset $A\subseteq C$ with $A+A$ Bernstein in $I$.


Download Citation

Krzysztof Ciesielski. Hajrudin Fejzić. Chris Freiling. "Measure Zero Sets with Non-Measurable Sum." Real Anal. Exchange 27 (2) 783 - 794, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 2 June 2008

zbMATH: 1048.28001
MathSciNet: MR1923168

Primary: 26A21 , 28A05

Keywords: algebraic sum , measurability , sets

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 2 • 2001/2002
Back to Top