Theorems · Theorem · measure theory
MeasureTheory.Measure.haveLebesgueDecomposition_spec
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [h : μ.HaveLebesgueDecomposition ν],
Measurable (μ.rnDeriv ν) ∧ (μ.singularPart ν).MutuallySingular ν ∧ μ = μ.singularPart ν + ν.withDensity (μ.rnDeriv ν)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
- MeasureTheory.Measure.singularPartstatement · cited by 71
- MeasureTheory.Measure.HaveLebesgueDecomposition.lebesgue_decompositionproof · cited by 6
- MeasureTheory.Measure.singularPart_defproof · cited by 5
- MeasureTheory.Measure.rnDeriv_defproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.mutuallySingular_singularPartproof · cited by 27
- MeasureTheory.Measure.eq_singularPartproof · cited by 6
- MeasureTheory.Measure.eq_withDensity_rnDerivproof · cited by 1
- MeasureTheory.Measure.rnDeriv_mul_rnDeriv'proof · cited by 0