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Homework Help: Fat Cantor set

  1. Dec 27, 2008 #1
    What is the definition of a fat cantor set? How do I show that the fat cantor set has positive Lebesgue measure and does not contain any interval.

    I know for the cantor set that at each stage, we remove the middle third of each interval starting with [0,1]. I am wondering if instead for the fat Cantor set, there is maybe a sequence of positive numbers {cn} and at the stage n, we need to remove the middle cnth of each interval but in this case, should the cn be odd?
    I know how to prove that the cantor set has measure 0 and that it contains no interval, but I am not sure how to proceed for the fat cantor set.
  2. jcsd
  3. Dec 27, 2008 #2


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  4. Dec 27, 2008 #3
    Thanks, that is very helpful.
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