Does a Set with Empty Interior Have Measure Zero?

ak416 · Mar 17, 2007

does a set with empty interior have measure zero? I think it does...

DeadWolfe · Mar 17, 2007

Doesn't the Cantor set have empty interior?

ak416 · Mar 18, 2007

ya and I read somewhere that it has measure zero. So this wouldn't be a counterexample.

ak416 · Mar 18, 2007

ok i may be wrong on this...

JasonRox · Mar 18, 2007

The Cantor set does have an empty interior and also has measure zero.

I never worked with measurable spaces yet, but if I had to guess, I would say a set with empty interior does in fact have measure zero.

ak416 · Mar 18, 2007

no actually it says in my book that the standard middle thirds cantor set has measure zero, but not any cantor set. So I guess its incorrect.

mathwonk · Mar 18, 2007

come on guys, look at the set of irrational numbers between 0 and 1. what is the interior? what is the measure?

take your book and put it under your coffee cup while you think about this.

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