Results 1 to 4 of 4

Math Help - Questions about contents on an algebra of set X

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    32

    Questions about contents on an algebra of set X

    Hi!

    I am totally new to measure theory, so bear in mind that all concepts like \sigma-algebra and  contents are new for me.
    Problem:
    Suppose A is an algebra of subsets on X and  \mu and  \nu are two contents on A such that  \mu \leq \nu and  \mu(X) = \nu(X) < \infty . Prove that  \mu = \nu .

    Im not sure how to start.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jan 2009
    Posts
    56
    Well if you mean by contents concentration or measure, then I think it's easy.
    Assume \nu(B)> \mu(B), this is for every B in the algebra A of X, A must include X as a subset if it's a sigma algebra (because this is an algebra which is closed to finite intersection of subsets of X, and also countable union if I remember correcly), which is a contradiction to the fact that  \nu(X)=\mu(X).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2010
    Posts
    32
    Okay, so I choose B = X , but we have that \mu(X) = \nu(X) , so we have a contradiction?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2009
    Posts
    56
    Yes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. If you want to box your contents
    Posted in the Math Forum
    Replies: 0
    Last Post: October 14th 2010, 10:47 AM
  2. Please help with these Algebra questions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 8th 2010, 02:13 PM
  3. algebra 3-4 only 3 questions..
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 3rd 2009, 12:21 AM
  4. Table of Contents help.
    Posted in the LaTeX Help Forum
    Replies: 0
    Last Post: November 25th 2008, 11:08 PM

Search Tags


/mathhelpforum @mathhelpforum