Does a Set with Empty Interior Have Measure Zero?

  • #1
122
0
does a set with empty interior have measure zero? I think it does...
 
  • #2
Doesn't the Cantor set have empty interior?
 
  • #3
ya and I read somewhere that it has measure zero. So this wouldn't be a counterexample.
 
  • #4
ok i may be wrong on this...
 
  • #5
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
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
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.
 

Suggested for: Does a Set with Empty Interior Have Measure Zero?

Replies
3
Views
775
Replies
21
Views
716
Replies
1
Views
572
Replies
8
Views
1K
Replies
1
Views
789
Replies
14
Views
2K
Replies
2
Views
827
Back
Top