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. > > -- > > > ---------------------------------------------------------------------------- > 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 a topic in the > Google Groups "Everything List" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/everything-list/1NWmK1IeadI/unsubscribe. > To unsubscribe from this group and all its topics, 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. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 stephe...@provensecure.com http://www.provensecure.us/ “This message (including any attachments) is intended only for the use of the individual or entity to which it is addressed, and may contain information that is non-public, proprietary, privileged, confidential and exempt from disclosure under applicable law or may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify sender immediately and delete this message immediately.” -- 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.