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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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William Elliot

Posts: 600
Registered: 1/8/12
Measure and Density
Posted: Feb 16, 2013 9:33 PM
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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?

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