See below (01)
Sean Barker
Bristol, UK (02)
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> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Waclaw Kusnierczyk
> Sent: 19 June 2007 09:44
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Probabilistic Ontologies
>
>
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> Barker, Sean (UK) wrote:
> > Waclaw
> >
> > From the point of view of practical mathematics,
> probability over
> > continuous distributions is defined through probability density
> > functions, with the probability for any interval being the
> integral of
> > the pdf over that interval. If you reduce the interval to
> zero, then
> > the probability goes to zero. No problem there.
>
> Depends on what you mean by 'reduce to zero'. There is the
> empty interval, and infinitely many singleton intervals
> [x,x]. For the empty interval, obviously P(X = x | x in the
> empty interval) = 0. For any singleton interval, it is not
> that obvious to me that P(X = x) = 0 for some x for which the
> 'reduced to zero' interval [x,x] is considered. (04)
Reduce to 0: for any sequence of intervals In = [xn, yn], xn, yn in
Reals, xn < yn, for arbitrary epsilon > 0, there exists N such that for
all n > N (yn - xn) < epsilon. (05)
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