Re: [boost] [random][rational] Is there any standard way to generate a random rationals?

Subject: Re: [boost] [random][rational] Is there any standard way to generate a random rationals?
From: MJanes (max.jns_at_[hidden])
Date: 2015-03-10 04:18:57

Il giorno giovedì 5 marzo 2015 22:39:54 UTC+1, Damian Vicino ha scritto:
>
> I was thinking the same approach. 
> But it is necessary to study how the selection affects the distribution. 
>

I don't think there exists such a thing as a "uniformly distributed 
rational" in some bounded interval; IOW, there's no way of defining a 
probability measure ( aka a totally additive bounded measure over a sigma 
algebra of subsets ) over a bounded interval of rationals uniformly with 
respect to the measure of the corresponding real interval ( indeed, note 
that the set of rationals in [0,1] has Lebesgue measure zero, that is, the 
probability that a unfirom real in [0,1] is rational is zero ). It's 
somewhat like asking for a *uniformly* distributed integer over 
[0,1,2...,+inf).

Of course, this does not mean there isn't a probability distribution of 
rationals satisfying some special *uniformness* criteria that fits your 
needs, but not in any *standard* way ....