Simple question

  • Thread starter ak416
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  • #1
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does a set with empty interior have measure zero? I think it does...
 

Answers and Replies

  • #2
453
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Doesn't the Cantor set have empty interior?
 
  • #3
122
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ya and I read somewhere that it has measure zero. So this wouldnt be a counterexample.
 
  • #4
122
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ok i may be wrong on this...
 
  • #5
JasonRox
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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.
 
  • #6
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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.
 
  • #7
mathwonk
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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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