[FOM] outer measure of a non-measurable set

[Monroe Eskew]

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).

Monroe