Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Measure space

  1. Aug 5, 2007 #1
    1. The problem statement, all variables and given/known data

    A, B in a sigma algebra

    Prove
    m(A)+m(B)=m(AuB)+m(AnB)

    m denotes the measure.

    3. The attempt at a solution

    Don't see how to do it.

    Somehow we are dealing with each individual set and taking the measure on them. Then finding what they equate to.
     
  2. jcsd
  3. Aug 5, 2007 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    A measure is additive on countable disjoint unions. So have you tried to write A[itex]\cup[/itex]B as a union of disjoint sets?

    (Note: I'm assuming m is a finite measure, i.e. does not take on infinity.)
     
    Last edited: Aug 5, 2007
  4. Aug 12, 2007 #3
    Ok you haven't tried hard Pivoxa
    Hint:
    use [tex] A= [A - (A \cap B)] \cup (A \cap B) \hspace{10pt}\text{or}\hspace{10pt} B= [B - (A \cap B)] \cup (A \cap B)[/tex] and see what you get from it.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook