Theorems · Theorem · measure theory

MeasureTheory.Measure.singularPart_add

∀ {α : Type u_1} {m : MeasurableSpace α} (μ₁ μ₂ ν : MeasureTheory.Measure α) [μ₁.HaveLebesgueDecomposition ν]
  [μ₂.HaveLebesgueDecomposition ν], (μ₁ + μ₂).singularPart ν = μ₁.singularPart ν + μ₂.singularPart ν

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue

Cited by

2 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.Measure.HaveLebesgueDecompositionMeasureTheory.Measure.HaveLebesgueDecomposition