How about conditional probabilities? If E1 is a proper subset of E2, and both E1 and E2 are measuarable and have probability zero, it is possible that the conditional probability P(E1 | E2) is strictly less than one.
So in some sense we may say that E1 is "less probable" than E2. Btw, I have deleted the groups "sci.physics" and "sci.math" for "newsgroups" and "followup to". In sci.stat.math Gabriel Chime <[EMAIL PROTECTED]> wrote: > Is there a nonstandard way to describe and compare probabilities of > measure zero sets? > Let's pick a real number, x, with uniform distribution. > Then let > p0 = P(x = 0), > pr = P(x is rational). > Then, p0=pr=0, yet my intuition tells me that pr > p0. > Is there a way of assigning infinitesimal (hyperreal) probabilities > s.t. > epsilon > pr > p0 >= 0 for all real positive epsilon? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
