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Math Help - Measurable Set

  1. #1
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    Measurable Set

    Hello,

    If X and Y are closed sets

    Then prove that X + Y is an F-sigma set

    Note : X + Y = { k in R^n : k = x + y for x in X and y in Y}

    Thanks a ton!
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  2. #2
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    Quote Originally Posted by unit1 View Post
    Hello,

    If X and Y are closed sets

    Then prove that X + Y is an F-sigma set

    Note : X + Y = { k in R^n : k = x + y for x in X and y in Y}

    Thanks a ton!
    Let { p_n} be a dense subset of X (for example a set of points with rational co-ordinates) and { q_n} be a dense subset of Y

    Then I claim that:

     X + Y = \bigcup_{i=1}^\infty(Y+p_i)\cup(X+q_i)
    Last edited by southprkfan1; April 19th 2010 at 06:43 AM.
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  3. #3
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    Hey thanks for that!

    I was wondering if it would also work with closed bounded subsets, as in compact subsets?
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