Getting the domain/support of objects, and domain type hierarchy

We currently don't have a common function to query the domain or support of something (a distribution, measure, ML model, etc.) yet, right? We could add something like getdomain(something) and getsupport(some_function)

For functions, the situation is more tricky since their domain/support will often not only depend on the argument type, but also on the actual shape of the argument (array sizes, etc.). We could do getdomain(f, shp::ValueShapes.AbstractValueShape) for the kind of stuff ValueShapes currently covers (could extend that).

Distributions currently offers support, but it's limited to univariate distributions. Having getdomain/getsupport in DomainSets would allow packages to add support for complex types of domains in a clean fashion without depending on DomainSets.

Would a getdomain/getsupport API be welcome in DomainSets (I could do a PR)?

(Edit: Also some discussion about domain/set type hierarchies further down.)

Start by reviewing the existing support API in Distributions and the ValueShapes.AbstractValueShape approach described in the issue. Resolve the API and domain/set hierarchy questions in the discussion, then define completion around an agreed getdomain/getsupport interface covering the stated distribution, measure, model, and function cases.