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: How to show something is a sigma-algebra

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data
    I was reading this Wiki article: http://en.wikipedia.org/wiki/Sigma-algebra and don't quite understand one of the examples.

    "The collection of subsets of X which are countable or whose complements are countable (which is distinct from the power set of X if and only if X is uncountable.). This is the σ-algebra generated by the singletons of X."

    2. Relevant equations
    1. Σ is not empty,
    2. Σ is closed under complements: If E is in Σ then so is the complement (X \ E) of E,
    3. Σ is closed under countable unions: The union of countably many sets in Σ is also in Σ.

    3. The attempt at a solution
    I kind of understand sigma-algebra, but I really don't get this example... If it's the sigma-algebra generated by singletons, then how can the first property be satisfied?
  2. jcsd
  3. Mar 11, 2010 #2
    Re: Sigma-algebra

    Nevermind, I figured it out. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook