Real Analysis Exchange

A converse to a theorem of Steinhaus

Yevgeny V. Mospan

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 291-294.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516816

Mathematical Reviews number (MathSciNet)
MR2218844

Zentralblatt MATH identifier
1142.28303

Subjects
Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

Keywords
absolute continuity singular measures difference set

Citation

Mospan, Yevgeny V. A converse to a theorem of Steinhaus. Real Anal. Exchange 31 (2005), no. 1, 291--294. https://projecteuclid.org/euclid.rae/1149516816


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