1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about measure zero

  1. Oct 29, 2006 #1
    I saw this come up in a proof: Since A is a Jordan measurable set (bd(A) has measure zero), there exists a closed rectangle B s.t A subset of B. So basically theyre saying, if bd(A) has measure zero then A is bounded. Can someone give me a quick proof of that? By the way when i say a set S has measure zero i mean for every e>0 there is a cover {U1,U2,...} of S by rectangles s.t. sum(i=1 to infinity)(volume(Ui)) < e.
     
  2. jcsd
  3. Oct 29, 2006 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Jordan measure only applies to bounded sets.
     
  4. Oct 29, 2006 #3
    o ok my bad. But in general, if you have any set with its boundary being of measure zero, it doesnt necessarily mean its bounded right?
     
  5. Oct 30, 2006 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You are correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Question about measure zero
  1. Measure zero (Replies: 9)

Loading...