Continuity Property for Non-increasing Sets (Probability)

1. Nov 28, 2007

rbzima

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. Nov 28, 2007

Office_Shredder

Staff Emeritus
It might help if you said what you were trying to prove

3. Nov 28, 2007

rbzima

Ahhh, good call my brother! Forgot!

Probability of the limit as n approaches infinity of $$E_{n}$$ equals the limit as n approaches infinity of the probability of $$E_{n}$$

4. Nov 28, 2007

mathman

The intersection of disjoint sets is empty!!!!!! All you need is 2 sets to get the result - Prob(empty set)=0.

5. Nov 29, 2007

rbzima

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.

6. Nov 29, 2007

rbzima

Nevermind everone! I just realized that I can still use disjoint sets and complementary probabilities of unions. Thanks for the different opinions though!