[FOM] outer measure of a non-measurable set
Ashutosh
ashu1559 at gmail.com
Thu Mar 28 10:44:17 EDT 2013
It can take any value between 0 and 1. This follows from:
For each 0 < x <= 1, one can construct a full outer measure subset of
[0, x] which meets each equivalence class in [0, 1]/~ at exactly one
point. One way of doing this is to ensure that it meets every perfect
subset of [0, x].
Ashutosh
On Thu, Mar 28, 2013 at 1:20 AM, 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
>
> Martin Davis
> Professor Emeritus, Courant-NYU
> Visiting Scholar, UC Berkeley
> eipye + 1 = 0
>
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