|
|
Denis Feldmann wrote:
> Here is what comes closest to HdB "ideas" : take a non standard integer
> N ("infinite", ie greater than all standard ones, of course). Define
> the measure of a standard set of integers A as p(A)= the sum of 1/N for
> all n <N in A* (A* is the extension of A to the non-standard integers)
> For instance, p("n is even")= 1/2 or 1/2-1/N according as N is even or
> odd; and the shadow of p(A), p°(A), is a real having "almost" the
> properties of a probability (could it be the density :-)), while p(A)
> *is* (of course) a discrete measure... and so additive. Note that with
> this definition, p(n=42)=1/N and the shadow p°(n=42)= 0, according to
> HdB "intuitions". Note also that the main point of contention (ie p(A),
> or p°(A)are nor probabilities (ie not countably additive)) is somewhat
> shunted...
We've already been round this one once (or possibly more than once).
But I guess that somebody else making another attempt can't
hurt. Well, it can't hurt me, and that's my principal concern :-)
|
|