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

[root]

Wolfgang,

In type terms it appears you want a new domain that is predicated on
3 things (S, F, and P). First you need to decide the name of the new 
domain e.g.

ProbabilitySpace(S: DomOrCat, F: DomOrCat, P: DomOrCat)

second you need to decide 
  if S is required to be a specific domain (say, your SpecialSampleSpace) or 
  can be a general category which either you 
    create SampleSpaceCategory from which SpecialSampleSpace is derived or
    is an existing category (say, Ring)
similarly for F and P. 

third, you need to define what a sample space is, what a sigma-field is,
and what category of maps you will allow.

Fourth, if you are making a Domain you need to decide on what representation
to have for elements of the domain. If you just want a collection of functions
(which Axiom calls a Package) then you don't need to worry about this. If you
plan to create many kinds of ProbabilitySpaces then you probably want a
category first.

Is S going to be a set? Does it have to be ordered?
Is F a set of elements out of S and thus has to be the same domain?
Is P required to implement maps P(S)->F that need to be conditioned on S and F?

This is very general as I'm not sure of your details but feel free to ask
more questions or send code and I'll try to help.

Tim Daly
address@hidden
address@hidden