On Dec 26, 5:50 am, gus gassmann <g...@nospam.com> wrote: > On 25/12/2012 5:57 AM, Butch Malahide wrote: > > > Did anyone say anything about wishing sets of equal cardinality all to > > have the same probability? > > The subject line says "uniform distributions". What can that mean OTHER > than "sets of equal cardinality have equal measure"?
In the case of the continuous uniform distribution on the interval [0,1], it means that "intervals of the same length have equal measure." All intervals have the same cardinality, but their measures vary.
I'm not sure what it means for a (finitely additive) measure on N. Perhaps, that all points have equal measure (which would have to be zero)? Or that sets of the same natural density should have equal measures? Maybe it should be translation-invariant?
> > 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. > > Bingo.