W^3
Posts:
29
Registered:
4/19/11


Re: Measure and Density
Posted:
Feb 19, 2013 2:39 PM


In article <Pine.NEB.4.64.1302161828050.5815@panix2.panix.com>, William Elliot <marsh@panix.com> wrote:
> 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? >
More interesting is to require 0 < m(S /\ I) < m(I) for all nonempty open intervals I contained in (0,1).

