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. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au Latest project: The Amoeba's Secret (http://www.hpcoders.com.au/AmoebasSecret.html) ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.