
Re: Continuous and discrete uniform distributions of N
Posted:
Dec 25, 2012 4:57 AM


On Dec 25, 3:12 am, Virgil <vir...@ligriv.com> wrote: > In article > <f9fb82dea07142f1b393a3e689c24...@c16g2000yqi.googlegroups.com>, > Butch Malahide <fred.gal...@gmail.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 oneelement subsets? > > If the space is N, it doesn't, which is teh point I was trying to bring > to your attention.
You said "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." If the probability space is the unit interval with Lebesgue measure, your "standard requirement" fails in the case of the partition into oneelement sets.
> > 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.
Did anyone say anything about wishing sets of equal cardinality all to have the same probability? Is that what the OP was talking about? I didn't try to read his post, as it seemed kind of obscure. Of course it's not possible, in an infinite sample space, for sets of the same cardinality all to have the same probability. (I'm assuming the axiom of choice, so I don't have to worry about Dedekindfinite infinite sets.)

