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Definition of a sigma-algebra

  1. Apr 21, 2005 #1
    Given the definition of a sigma-algebra, I need to show that the intersection of a sequence of elements in a sigma-algebra is in the sigma-algebra:

    Let F be a sigma-algebra, then:
    1) The empty set is in F.
    2) If A is in F, then so is the complement of A.
    3) The union of a sequence of elements in F is also in F.

    To prove:
    The intersection of a sequnce of elements in F is also in F.

    I'm quite stuck and seem to go around in circles. Any help on how to attack this problem would be appreciated.
  2. jcsd
  3. Apr 21, 2005 #2

    matt grime

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    Take an intersection AnBnC... what is its complement?
  4. Apr 21, 2005 #3
    Right, the intersection is the union of the complements. And since the complements, and therefore the union, are in F, the intersection must also be in F.
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