"kir" <email@example.com> wrote in message news:firstname.lastname@example.org... On Sunday, November 11, 2012 4:18:15 PM UTC-5, Ray Vickson wrote: > On Sunday, November 11, 2012 7:38:09 AM UTC-8, kir wrote: > >>> > What kind of work is being done in probability theory beyond the >>> > standard normally used? I know that negative >>>probabilities have >>> > been discussed. Is there anything else? > > > >> I'm not sure this is what you want, but there has been work in >> Probability theory using "non-standard analysis", so >one can talk about >> actual infinitesimals, etc. Perhaps the most accessible introduction to >> this is the old but still >good >little book by Edward Nelson ("Radically >> Elementary Probability", Princeton U. Press). You can download a >free >> pdf >version from Edward Nelson's home page: just go to his publications >> list and click on the book title. > > >> >> RGV
>Primarily dealing with nonstandard analysis. I suppose I really need to >study measure theory before I can dive in too >deep. Dealing with >infinitesimals is a great extension in my opinion. It always bothered me >that we often define >something with probability zero to mean it can't >occur, yet even though in the case of an infinite probability >distribution > >X P(X=x) = 0 for all x values. One x value DOES occur.
>What's really true is that it occurs with infinitesimal probability.
better yet, look for error ball of radius approaching zero.