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Butch Malahide wrote:
> eugene wrote:
> > Could you please explain how are you going to choose c disjoint
> > non-measurable sets.
>
> Use transfinite induction to construct c disjoint sets X_t, each having
> nonempty intersection with every closed set of positive measure. This
> can be done because there are only c closed sets of positive measure,
> and every such set contains c points. (That should be enough of a hint
> if you're familiar with transfinite induction; if not, I could provide
> more details.)
Could you please provide more details ? I know what a transfinite
induction is, but i've never
used it on my own and am not able to apply it in our case.
Thanks.
>Now X_t is nonmeasurable because neither it nor its
> complement contains a closed set of positive measure.
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