Continuity Property for Non-increasing Sets (Probability)

[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!

 

[Office_Shredder]

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

 

[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 $$E_{n}$$

 

[mathman]

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

 

[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.

 

[rbzima]

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