JuliaMath / JuliaMath/MeasureBase.jl
Use DomainSets.jl?
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Description
Our [domains.jl](https://github.com/cscherrer/MeasureBase.jl/blob/master/src/domains.jl) is currently kind of hacked together. When I wondered about replacing this with ManifoldsBase, @gdalle reminded me about DomainSets.jl:
> Just popping by to mention [https://github.com/JuliaApproximation/DomainSets.jl](https://github.com/JuliaApproximation/DomainSets.jl) as part of the discussion of `AbstractDomain`s.
>
> _Originally posted by @gdalle in https://github.com/cscherrer/MeasureBase.jl/issues/7#issuecomment-906761492_
Funnily enough, we had some brief discussion about this three years ago [here](https://github.com/JuliaApproximation/DomainSets.jl/issues/32).
There are a few places domains come up, though we don't currently have a uniform interface for managing them
1. For determining a bijection to a real vector space
2. To anticipate error conditions in `logdensity` and replace these cases with `-Inf`
3. With `⊆`, for `≪` computations (nested supports are necessary for absolute continuity)
4. With `∩` for supports of pointwise product (`⊙`)
5. With `∪` for superposition (`+`)
Some potential concerns:
1. Can this play nice with ManifoldMeasures? (cc @sethaxen)
2. DomainSets currently depends on `StaticArrays`, which is a heavy dependency for a core library like this. Would it be possible to refactor DomainSets somewhat to use Static.jl instead, possibly with an optional StaticArrays dependency? Or maybe there's a better approach? (This part should probably be a new issue in DomainsSets, cc @daanhb @dlfivefifty)
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