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!

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

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    mathman

    User Avatar
    Science Advisor
    Gold Member

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Continuity Property for Non-increasing Sets (Probability)
  1. Set of continuities (Replies: 4)

  2. Continuous probability (Replies: 2)

Loading...