Adds mass and normalize for a measure

src/MeasureTheory.jl

@@ -30,6 +30,8 @@ export basemeasure
 
 export as
 
+export mass, logmass, is_probability_measure, normalize
+
 abstract type AbstractMeasure end
 
 sampletype(μ::AbstractMeasure) = typeof(testvalue(μ))
@@ -54,6 +56,7 @@ include("absolutecontinuity.jl")
 include("parameterized.jl")
 include("macros.jl")
 include("resettablerng.jl")
+include("mass.jl")
 
 include("primitive.jl")
 include("primitives/counting.jl")

src/combinators/weighted.jl

@@ -20,6 +20,8 @@ function logdensity(sm::AbstractWeightedMeasure, x)
     logdensity(sm.base, x) + sm.logweight
 end
 
+logmass(d::AbstractWeightedMeasure) = logmass(d.base) + d.logweight
+
 ###############################################################################
 
 struct WeightedMeasure{R,M} <: AbstractWeightedMeasure

src/distributions.jl

@@ -35,6 +35,10 @@ end
 
 ∫(::typeof(identity), ::Dists.Distribution) = 1.0
 
+# all Distributions distributions are probability measures
+logmass(μ::DistributionMeasure) = true
+is_probability_measure(μ::DistributionMeasure; kwargs...) = true
+
 logdensity(μ::Dists.Distribution, x) = Dists.logpdf(μ,x)
 Dists.logpdf(d::AbstractMeasure, x) = logdensity(d,x)
 

src/mass.jl

@@ -0,0 +1,40 @@
+using LinearAlgebra: LinearAlgebra
+
+"""
+    logmass(μ::AbstractMeasure)
+
+Compute the logarithm of the [`mass`](@ref) of the measure ``μ``.
+"""
+function logmass end
+
+"""
+    mass(μ::AbstractMeasure)
+
+Compute the mass of the measure ``μ``.
+
+That is, given a set ``S`` with elements ``x ∈ S``, compute
+``μ(S) = ∫_S dμ(x)``.
+
+!!! note
+    This function should not be directly modified. Instead, developers should
+    overload [`logmass`](@ref).
+"""
+mass(μ) = Exp(logmass(μ))
+
+"""
+    normalize(μ::AbstractMeasure)
+
+Convert the measure ``μ`` to a probability measure, that is, a measure whose
+total mass is 1.
+"""
+LinearAlgebra.normalize(μ::AbstractMeasure) = μ * inv(mass(μ))
+
+"""
+    is_probability_measure(μ::AbstractMeasure; kwargs...) -> Bool
+
+Return `true` if ``μ`` is a probability measure, that is, a measure whose
+total [`mass`](@ref) is 1.
+
+`kwargs` are forwarded to `isapprox`.
+"""
+is_probability_measure(μ; kwargs...) = isapprox(mass(μ), true; kwargs...)

src/primitives/dirac.jl

@@ -32,3 +32,5 @@ function logdensity(μ::Dirac{M}, ν::Dirac{M}, x) where {M}
         return -Inf
     end
 end
+
+logmass(μ::Dirac) = false