[Axiom-math] Sigma-Algebra (Sigma-Field)

[Wolfgang Zocher]

Hello all,

I am planning to install basic aspects of probability theory into AXIOM but
I'm not sure how to do that, esp. where to begin. When I look into my books on
probability theory and measure theory, they always begin with the definition
of a Sigma-Field or Sigma-Algebra with axioms based on sets. And exactly at
this point I have difficulties to find the appropriate point in the hierarchy
of categories, domains etc. in AXIOM where the new field or algebra should be
derived from. The same problem arises when I think of the concept of
probability space as a triple of (S, F, P) where S is the sample space, F is
the collection of events (the Sigma-Field) and P is a function that maps F
into the interval [0,1], the probability of events. Where in the hierarchy can
I place this P-space?

The reason for doing all this is that I plan to study certain aspects of
Brownian Movements preparing simulations written in Fortran or CL.

It would be wonderful if anyone could help me to bear down these hurdles..

Regards,
Wolfgang
--
Wolfgang Zocher  http://www.wolfgang-zocher.privat.t-online.de/
Registered Linux User #337888 using Debian GNU/Linux