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Homework Help: 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

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    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

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    You are correct.
     
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