In article <firstname.lastname@example.org>, Butch Malahide <email@example.com> wrote:
> On Dec 25, 12:48 am, Virgil <vir...@ligriv.com> wrote: > > > > The standard definition of probability requires that the sum of the > > probabilities over ANY set of sets making up a partition of the space be > > equal to one. > > How does that work out in the case of the partition of the space into > its one-element subsets?
If the space is N, it doesn't, which is teh point I was trying to bring to your attention.
> Are you saying that the standard definition > requires every probability distribution to be discrete?
Not at all! Finite spaces cause no problems and for a space of uncountable cardinality, one can have the probability of every countable set equal to zero and still have meaningful probability. It is only spaces of countable cardinality that cause this sort of trouble if one wishes sets of equal cardinality all to have the same probability. --