## Real Analysis Exchange

### A converse to a theorem of Steinhaus

Yevgeny V. Mospan

#### 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