Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple question

  1. Mar 17, 2007 #1
    does a set with empty interior have measure zero? I think it does...
  2. jcsd
  3. Mar 17, 2007 #2
    Doesn't the Cantor set have empty interior?
  4. Mar 18, 2007 #3
    ya and I read somewhere that it has measure zero. So this wouldnt be a counterexample.
  5. Mar 18, 2007 #4
    ok i may be wrong on this...
  6. Mar 18, 2007 #5


    User Avatar
    Homework Helper
    Gold Member

    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.
  7. Mar 18, 2007 #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.
  8. Mar 18, 2007 #7


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook