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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Measure and Density
Replies: 14   Last Post: Feb 23, 2013 11:26 AM

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W^3

Posts: 28
Registered: 4/19/11
Re: Measure and Density
Posted: Feb 19, 2013 2:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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).

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