A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

I need help please to prove some properties of a positive measure which are (a)Let µ be a positive measure on a measurable space (X,M). Let c > 0. Prove that ˜µ = cµ is also a measure (b) Let µ1, µ2 be two positive measures on a measurable space. Assume also that there is at least one set A ∈ M such that µ1(A) + µ2(A) < ∞. Prove that ˆµ = µ1 + µ2 is also a measure

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @oldrin.bataku could you help me with this question please?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is a good place to start http://www.math.uah.edu/stat/prob/Measure.html https://en.wikipedia.org/wiki/Measure_%28mathematics%29 but i still can't solve it!

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Given µ is a positive measure. Define cµ = c* (µ (A) ) , where A is a set . Claim: cµ is a positive measure Proof: 1. cµ ( ∅ ) = c * ( µ ( ∅ ) ) = c * 0 = 0 2. cμ(⋃i∈IAi)=∑i∈Icμ(Ai) cμ(⋃i∈IAi)=c⋅(μ(⋃i∈IAi))=c⋅∑i∈Iμ(Ai)=∑i∈Icμ(Ai)

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that correct for part a?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you should also show that scaling by \(c>0\) preserves nonnegativity but yes

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.