Simple question

[ak416]

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

 

[DeadWolfe]

Doesn't the Cantor set have empty interior?

 

[ak416]

ya and I read somewhere that it has measure zero. So this wouldnt be a counterexample.

 

[ak416]

ok i may be wrong on this...

 

[JasonRox]

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]

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]

come on guys, look at the set of irrational numbers betwen 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.