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Prove that this set has volume.

  1. Dec 2, 2011 #1
    1. The problem statement, all variables and given/known data
    Let D_k=(r_k-1/2^k,r_k+1/2^k), where r_k=1/k. Then prove that
    D=union_k=1 to ∞ (D_k) has volume.

    2. Relevant equations



    3. The attempt at a solution
    I tried to solve this problem by showing bd(D) has measure zero.
    So I wanted to show that bd(D) is contained in union_k=1 to ∞(bd(D_k)). Of course since bd(D_k)={r_k-1/2^k, r_k+1/2^k}, union_k=1 to ∞(bd(D_k)) has measure zero. But how can I show this? Or is there another solution to this problem?
     
  2. jcsd
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