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