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Math Help - Subspace

  1. #1
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    Subspace

    Show: If U is a subspace of R^n with dimension k<n, then U is a null set (measure theory).
    Last edited by TXGirl; April 15th 2008 at 05:01 AM. Reason: Correction
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  2. #2
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    Quote Originally Posted by TXGirl View Post
    Show: If U is a subspace of R^n with dimension k<n, then U is an empty set.
    Not true! Consider the cartesian plane \mathbb{R}^2, any line through origin is a subspace and has dimension 1 (which is less than 2).Its a non empty set.
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    Not true! Consider the cartesian plane \mathbb{R}^2, any line through origin is a subspace and has dimension 1 (which is less than 2).Its a non empty set.
    Quote Originally Posted by TXGirl View Post
    Show: If U is a subspace of R^n with dimension k<n, then U is a null set (measure theory).
    She meant "null measurable set" not "empty set". This is still not true. I gave a counterexample to that already. Just consider a line segment. A line segment does not have null measure.
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