For MeasureTheory.jl, we need a nice way to represent some domains, like
- continuous sets
- Infinite discrete sets
- Also finite sets
a:b, but that’s easier
Eventually we’ll need to be able to represent measures on manifolds, either as in Manifolds.jl or as in Bijectors.jl or TransformVariables.jl. That’s further down the line, but I want to be sure to set things up in a way that doesn’t lead to headaches going forward.
To be a little more specific, we define most measures in terms of a density over some base measure. The most common of these is
Lebesgue(X) for some
We’ve been using
Lebesgue(Real) for a while, but…
- The type hierarchy approach is kind of rigid, for example getting in the way of things like symbolic evaluation
- There’s not a clean way to have subsets like
We could build
𝕀 as part of MeasureTheory, but I want to be sure we can play nice with other packages, especially
Manifolds.jl and the
What’s a good approach to keep consistency with these packages?