Date: Feb 16, 2013 9:33 PM Author: William Elliot Subject: Measure and Density Topology Q+A Board Ask An Analyst

How can we find a measurable dense subset S of [0,1], with m(S) < 1,

and such that for any (a,b) in [0,1], we have m(S /\ (a,b)) > 0?

I have thought of fat Cantor sets, but I cannot see well how to

do it. Any suggestions, please?