Results 1 to 2 of 2

Math Help - Sigma algebra of infinite sets.

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    6

    Sigma algebra of infinite sets.

    I'm having trouble with this problem, please help:

    Let Ω be a uncountable set. Let S be the collection of subsets of Ω given by: AS if and only if A is finite or infinite countable or A complement is finite or infinite countable. Show that S is a σ-algebra
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by LAINHELL View Post
    I'm having trouble with this problem, please help:

    Let Ω be a uncountable set. Let S be the collection of subsets of Ω given by: AS if and only if A is finite or infinite countable or A complement is finite or infinite countable. Show that S is a σ-algebra
    Note that \emptyset,\Omega\in S (Why? Hint: see the definition of S).

    Now, if A\in S, is A^c\in S? (To show this, you just mess around with the definition of S.)

    Last, you want to show that if \{A_i\} is a collection of sets in S, then \bigcup A_i\in S (what have you tried?)

    Please show some work so we can have a better idea of where to help you.

    Does this makes sense?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lebesgue measure on sigma-fields of Borel sets
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 27th 2011, 07:56 PM
  2. Sigma-algebra
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 26th 2011, 12:03 PM
  3. Replies: 1
    Last Post: February 4th 2011, 08:39 AM
  4. Show intersection of sigma-algebras is again a sigma-algebra
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 20th 2010, 07:21 AM
  5. Finding the smallest sigma algebra containing two sets
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 18th 2009, 10:33 PM

Search Tags


/mathhelpforum @mathhelpforum