1. Limited time only! Sign up for a free 30min personal 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!

Probability help/sigma-algebras

  1. Oct 20, 2011 #1
    Let (S, ε, P) be a probability space and let A be an element of ε with P(A)>0. Let F={AπE :E is an element of }
    -Prove that F is a sigma-algebra on A.

    Not sure even where to go with this really. I know that to be a sigma-algebra has to be closed under complementation and countable unions. I'm not very good with proofs, and just a push in the right direction would help me out a ton
  2. jcsd
  3. Oct 21, 2011 #2
    I assume that F is supposed to be

    [itex]F:=\left\{A\cap E: E\in\epsilon\right\}[/itex].​

    Now, for F to be a sigma-algebra on A, you have to first show that [itex]F\subseteq 2^A[/itex]. Then, show that the following 3 conditions are satisfied by F.

    1. [itex]\emptyset,A\in F[/itex]

    • If [itex]B\in F[/itex], then it is necessary that [itex]B^c\in F[/itex]

    • For every sequence of sets [itex](B_n)[/itex], where everyone of them is a member of F, it is necessary that [itex]\bigcup_{n\in\mathbb{N}}B_n\in F[/itex].

    Try to prove the conditions one-by-one. Also use the fact that [itex]\epsilon[/itex] is a sigma-algebra. If you have some more questions, feel free to ask.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Probability help/sigma-algebras
  1. Sigma Algebras (Replies: 15)

  2. Sigma Algebras (Replies: 1)

  3. Sigma Algebras (Replies: 3)

  4. Sigma Algebra (Replies: 11)