Hi Russell,
Ah! I don't quite grok it completely, but thank you for this example. We
had to assume an already existing measure on the Reals. Where does that
come from?
On Mon, Jun 30, 2014 at 9:38 PM, Russell Standish <li...@hpcoders.com.au>
wrote:
> On Mon, Jun 30, 2014 at 08:32:37PM -0400, Stephen Paul King wrote:
> > Hi Russell,
> >
> > I don't get it. How does the constraint of a finite sample overcome
> the
> > inherent zero measure?
> >
>
> Because a finite constraint matches an infinite number of zero measure
> items.
>
> Consider the set of real numbers matching the constraint that the
> initial sequence in the binary expansion is 0.1100111100111
>
> Even though each real number has measure zero, the set of all numbers
> matching that constraint has measure 2^{-13} (about 0.000122).
>
> Assuming the standard measure on the reals, of course.
>
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