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Borel Measureable Functions

  • 20-05-2007 8:42pm
    #1
    SGKM
    Registered Users, Registered Users 2 Posts: 207 ✭✭


    I'm doing an exam in financial maths on Tuesday morning and I'm wondering if anyone can tell me if g(x)=x is Borel Measureable?


Comments

  • #2
    Son Goku
    Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    Yes, it is as Borel Measurable as they get, being both monotonic and continuous.


  • #3
    SGKM
    Registered Users, Registered Users 2 Posts: 207 ✭✭SGKM


    Thanks, I had the exam yesterday morning and I had to prove that if f:R->R f' is Borel. I gave it an attempt but it was tougher than I had thought!


  • #4
    Son Goku
    Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    SGKM wrote:
    Thanks, I had the exam yesterday morning and I had to prove that if f:R->R f' is Borel. I gave it an attempt but it was tougher than I had thought!
    I wouldn't worry too much, in those kind of questions they're usually just looking to see if you understand how proving something is Borel Measurable works, they usually don't care whether you actually do prove it.


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