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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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
Latest project: The Amoeba's Secret
(http://www.hpcoders.com.au/AmoebasSecret.html)
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