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| ``Re: Possible Counterexample''
by vernondalhart on 2005-05-02 13:02:29 |
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| The theorem in question doesn't say that it necessarily 'cuts each piece in half'. It says it divides each A_i into two pieces of equal measure.
Now, if each A_i already is measure zero, then the two subsets of A_i - A_i itself, and the empty set qualifies as a perfect example of such a division. So if all your subsets are of measure zero, any hyperplane will work, because any hyperplane accomplishes this. |
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