Re: Probability of picking a positive rational number at random

On 2008-03-14, Ross A. Finlayson <raf@xxxxxxxxxxxxxxx> wrote:
[... "distribution" based on arbitrary well-orderings ...]
That's a random natural integer no different than uniformly random
from all the natural integers.

To make sense of this, start with the definition of a probability
distribution: a measure over a sigma-algebra of sets such that the
measure of the universal set is 1.

In particular, you start with the Lebesgue measure on the reals. Then
from each Lebesgue measurable set you construct a set of distributions
over the natural numbers via two arbitrary well-orderings (which had
better have the same order type).

Now, what are you doing with the measure over these sets of
distributions? That wasn't clear.


The rest of your post appeared to be based on false premises.


- Tim
.