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Continuity Property for Non-increasing Sets (Probability)

  1. Nov 28, 2007 #1
    So, I know the proof for a non-decreasing set using the continuity property, and I'm wondering if I have to use the intersection of all pairwise disjoint sets rather than the union, as seen in the non-decreasing proof. Any help would be greatly appreciated!
  2. jcsd
  3. Nov 28, 2007 #2


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    It might help if you said what you were trying to prove
  4. Nov 28, 2007 #3
    Ahhh, good call my brother! Forgot!

    Probability of the limit as n approaches infinity of [tex]E_{n}[/tex] equals the limit as n approaches infinity of the probability of [tex]E_{n}[/tex]
  5. Nov 28, 2007 #4


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    The intersection of disjoint sets is empty!!!!!! All you need is 2 sets to get the result - Prob(empty set)=0.
  6. Nov 29, 2007 #5
    Does anyone have any idea what this would look like in a Venn Diagram? I personally was thinking that I might be able to prove this using disjoint sets with unions, and complementary probabilities. I'm not 100% sure of that though at this point.
  7. Nov 29, 2007 #6
    Nevermind everone! I just realized that I can still use disjoint sets and complementary probabilities of unions. Thanks for the different opinions though!
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