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

Help with sigma-algebra prob, pls

  1. Sep 22, 2004 #1
    Here's what it says:

    "Let C be a collection of sets & E an element in the sigma-algebra generated by C. Then there is a countable subcollection C_0 contained in C such that E is an element of the sigma-algebra A_0 generated by C_0."
     
  2. jcsd
  3. Sep 22, 2004 #2

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    i suggest recalling the definition of a sigma algebra.

    i.e. for analogy, if A is a polynomial ring generated by a set S, and E is an element of A, then there is a finite subset T of S such that E belongs to the polynomial algebra generated by T.
     
  4. Sep 23, 2004 #3
    here's my definition:
    i) empty set is in C
    ii) if a set is in C then so is its complement
    iii) if a collection of sets is in C then so is the union of all those sets

    i guess with de morgan's laws intersections of sets are also in there, but i'm not sure how that helps.
     
  5. Sep 23, 2004 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    well it has been over 4 decades for me, but i do not recall your dfiniton as being corrct for sigma algebras. I think there is a countability assumption in there on those unions.

    you might check it. yeah, here is what I googled up:

    http://mathworld.wolfram.com/Sigma-Algebra.html
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Help with sigma-algebra prob, pls
  1. Sigma algebra? (Replies: 8)

Loading...