Open Access
1999/2000 On Openness of Density Points under Mappings
Harry I. Miller, Henry L. Wyzinski
Real Anal. Exchange 25(1): 383-386 (1999/2000).


Basu and Ganguly recently proved a theorem connected to the classical theorem of Steinhaus which states that $A - B$ has nonempty interior if $A$ and $B$ are Lebesgue measurable subsets of the real line, each having positive measure. The Basu and Ganguly paper deals with a particular 2-place function, namely $f(x,y) = x/y$. There is nothing special about ratios. We will extend their results to functions satisfying simple conditions on their partial derivatives. An $n$ dimensional analogue is also presented.


Download Citation

Harry I. Miller. Henry L. Wyzinski. "On Openness of Density Points under Mappings." Real Anal. Exchange 25 (1) 383 - 386, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.28002
MathSciNet: MR1758894

Primary: 28A05

Keywords: density points , Steinhaus theorem

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
Back to Top