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``Re: Possible Counterexample'' by bs on 2005-05-01 22:18:16
In your example, the part of A_i above the hyperplane and the part below the hyperplane both have measure 0, because A_i itself has measure 0.

Note that the part of A_i which intersects any given hyperplane always has measure 0 (because the hyperplane itself has measure 0), so is irrelevant. You can include this intersection in either part if you so like.
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