On Mar 12, 4:50 pm, FredJeffries <fredjeffr...@gmail.com> wrote: > On Mar 10, 11:36 am, "Peter Percival" <peterxperci...@hotmail.com> > wrote: > > > Is there a theory of probability in which probabilities do not lie in the > > real interval [0,1]? > > http://arxiv.org/abs/0912.4767 > > > More specifically, is there one in which the "space" > > of probabilities may have points x, y, z with x < y, x < z but y and z not > > necessarily comparable? > > Not sure what you mean by "not necessarily comparable", but in the > system of smooth infinitesimal analysis we have that if y and z differ > by an infinitesimal then the order relation does not satisfy the > trichotomy law: > (y < z) OR (y < z) OR (y = z) > > http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysishttp://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
If the infinitesimals of SIA haven't trichotomy, is there at least that a <= b or b <= a?
Then back to probabilities, it is rather nonstandard (and not with regards to the standardization of a distribution's parameter) in probability for a probability to not be within R_[0,1], with that the sum or integral of the mass/density function over the support space is one. (Bose/Fermi, parastatistics, anyonic)