Does a Set with Empty Interior Have Measure Zero?

ak416
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does a set with empty interior have measure zero? I think it does...
 
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Doesn't the Cantor set have empty interior?
 
ya and I read somewhere that it has measure zero. So this wouldn't be a counterexample.
 
ok i may be wrong on this...
 
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.
 
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.
 
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.
 

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