Density measures and Radon-Nikodym (#141)

* bugfix and tests

* bump version

Project.toml

@@ -1,7 +1,7 @@
 name = "MeasureTheory"
 uuid = "eadaa1a4-d27c-401d-8699-e962e1bbc33b"
 authors = ["Chad Scherrer <[email protected]> and contributors"]
-version = "0.10.2"
+version = "0.10.3"
 
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"

src/density.jl

@@ -71,19 +71,29 @@ basemeasure(μ::DensityMeasure) = μ.base
 
 logdensity(μ::DensityMeasure{F,B,Val{true}}, x) where {F,B} = μ.f(x)
 
+density(μ::DensityMeasure{F,B,Val{false}}, x) where {F,B} = μ.f(x)
+
+logdensity(μ::DensityMeasure{F,B,Val{false}}, x) where {F,B} = log(density(μ,x))
+
 export ∫
 
 """
-    ∫(f, base::AbstractMeasure; log=false)
+    ∫(f, base::AbstractMeasure)
 
-Define a new measure in terms of a density `f` over some measure `base`. If
-`log=true` (`false` is the default), `f` is considered as a log-density.
+Define a new measure in terms of a density `f` over some measure `base`.
 """
-∫(f, base::AbstractMeasure; log=false) = DensityMeasure(f, base, Val(log))
+∫(f, base::AbstractMeasure) = DensityMeasure(f, base, Val(false))
+
+∫(μ::AbstractMeasure, base::AbstractMeasure) = ∫exp(log𝒹(μ, base), base)
 
-∫(μ::AbstractMeasure, base::AbstractMeasure; log=false) = ∫(𝒹(μ, base), base; log=log)
 
 export ∫exp
+
+"""
+    ∫exp(f, base::AbstractMeasure; log=false)
+
+Define a new measure in terms of a density `f` over some measure `base`.
+"""
 ∫exp(f,μ) = DensityMeasure(f,μ,Val{true}())
 
 # TODO: `density` and `logdensity` functions for `DensityMeasure`

test/runtests.jl

@@ -388,3 +388,22 @@ end
         @test repr(Lebesgue(ℝ) ^ (3, 2)) == "Lebesgue(ℝ) ^ (3, 2)"
     end
 end
+
+@testset "Density measures and Radon-Nikodym" begin
+    x = randn()
+    let d = ∫(𝒹(Cauchy(), Normal()), Normal())
+        @test logdensity(d, x) ≈ logdensity(Cauchy(), x) 
+    end
+
+    let f = 𝒹(∫(x -> x^2, Normal()), Normal())
+        @test f(x) ≈ x^2
+    end
+
+    let d = ∫exp(log𝒹(Cauchy(), Normal()), Normal())
+        @test logdensity(d, x) ≈ logdensity(Cauchy(), x) 
+    end
+
+    let f = log𝒹(∫exp(x -> x^2, Normal()), Normal())
+        @test f(x) ≈ x^2
+    end
+end