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: Generating the Borel-algebra from half-open intervals

  1. Dec 8, 2011 #1
    Hi everybody!

    I have been asked to show that the Borel-algebra can be generated from the set of half-open intervals of the form [a , b) where a<b.

    I know that the set of open intervals of the form (a,b) where a<b generates the Borel-algebra and thought I would go about showing that the to sets generates the same δ-algebra. But that has proven more difficult than I thought.

    Can anybody give me an direction?


    Any help is greatly appreciated!
    dane502
     
  2. jcsd
  3. Dec 8, 2011 #2
    Can you write the open intervals as a union of halfopen intervals?

     
  4. Dec 8, 2011 #3
    Thank you for your answer.

    No, the half-open intervals has to be on the form of [a,b), so any union of those half-open intervals (that is not disjoint) will also have form [a,b).
     
  5. Dec 8, 2011 #4
    Sure of that?
     
  6. Dec 8, 2011 #5
    Think of

    [tex]\bigcup [a-1/n,b)[/tex]
     
  7. Dec 8, 2011 #6
    Thank you. Somehow I missed that.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...