[FOM] outer measure of a non-measurable set

Monroe Eskew meskew at math.uci.edu
Thu Mar 28 02:52:23 EDT 2013

On Mar 27, 2013, at 11:20 PM, Martin Davis <martin at eipye.com> wrote:

> A friend asked me. Can anything be said about the outer measure of a set containing one point from each equivalence class with respect to the relation x~y <=> x-y is rational, x,y in [0,1]?
> Martin

No.  By Vitali's argument, it must be positive. But let r>0.  For any x, there is a y such that x~y and 0<y<r.  So by the axiom of choice, we may choose a set of representatives which are all in (0,r).


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