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!

Homework Help: If u is a nonnegative, additive function, then u is countably subadditive

  1. Mar 4, 2012 #1
    I'm trying to prove the following:


    I ran into a roadblock at the end. I can't use the assumption that [itex]\mu[\itex] is additive because we don't know that [itex](\cup{A_k}) \cap A_{j + 1} = \emptyset[\itex].

    We do know that [itex]\mu(\cup_{k=1}^jA_k) + \mu(A_{j + 1} \leq \sum_{k=1}^{j+1}\mu(A_k)[\itex].
  2. jcsd
  3. Mar 8, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    You don't really need to worry about the intersection stuff. It's enough to note that a nonnegative additive function will be (finitely) subadditive.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook