Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

If E is countable. Let F be the power set of E. For some event A in F, is it true that the B_n below approximates A (as a Caratheodory extension)?

B_n = { [w(0),w(1),w(2),..,w(n)] : w in A }

I mean stronger, do B_n in a set theory sense converge to A?

share|improve this question
    
No. e.g. $A=\lbrace x\in\lbrace 0,1\rbrace ^{\mathbb N}\colon $x has density 1/3 of 1's$\rbrace$. –  Anthony Quas Oct 10 '12 at 18:29
    
Can you be a bit more precise? The Caratheodory extension is about measures, but I see no measure here. And what is convergence in a set theory sense? –  Michael Greinecker Oct 10 '12 at 22:10
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.