Adding pushforward measures

[oschulz]

A possible implementation would be a type PushforwardMeasure(f, μ) with a shorthand syntax ν = f.(μ) - this implies a monadic view of measures:

struct PushforwardMeasure{F,M} <: AbstractMeasure
    f::F
    orig::M
end

Random.rand(m::PushforwardMeasure) = m.f(rand(m.orig))

map(f, μ::AbstractMeasure) = PushforwardMeasure(f, μ)
Base.Broadcast.broadcasted(f, μ::AbstractMeasure) = map(f, μ)

[oschulz]

PushforwardMeasure would be a generalization of MeasureTheory.Affine.

f would be expected to support ChangesOfVariables.with_logabsdet_jacobian, and should support InverseFunctions.inverse as well if possible.

[cscherrer]

Ok, we already have
https://github.com/cscherrer/MeasureTheory.jl/blob/master/src/combinators/transforms.jl

But maybe it can be generalized beyond TransformVariables

[oschulz]

But maybe it can be generalized beyond TransformVariables

I think that would be very important now that we have ChangesOfVariables.jl as a community standard (designed as a companion for InverseFunctions.jl).

[cscherrer]

Pushforwards need some updates (see #125), but since there is an implementation I'll close this issue