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2005-2006 A converse to a theorem of Steinhaus
Yevgeny V. Mospan
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Real Anal. Exchange 31(1): 291-294 (2005-2006).


A result of H. Steinhaus states that any Lebesgue measurable set $X\subset R$ with positive Lebesgue measure has a property that its difference set contains an open interval around zero. In this note we will prove a statement, which, in a sense, complements it.


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Yevgeny V. Mospan. "A converse to a theorem of Steinhaus." Real Anal. Exchange 31 (1) 291 - 294, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1142.28303
MathSciNet: MR2218844

Primary: 28A75

Keywords: Absolute continuity , difference set , singular measures

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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