Theorems · Theorem · measure theory
MeasureTheory.Measure.HaveLebesgueDecomposition.lebesgue_decomposition
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [self : μ.HaveLebesgueDecomposition ν],
∃ p, Measurable p.2 ∧ p.1.MutuallySingular ν ∧ μ = p.1 + ν.withDensity p.2- Cited by
- 6 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 9,879
- Measurablestatement · cited by 1,499
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement · cited by 91
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.haveLebesgueDecomposition_specproof · cited by 6
- MeasureTheory.Measure.singularPart_defstatement and proof · cited by 5
- MeasureTheory.Measure.rnDeriv_defstatement and proof · cited by 4
- MeasureTheory.Measure.singularPart_smulproof · cited by 4
- MeasureTheory.Measure.lintegral_rnDeriv_lt_top_of_measure_ne_topproof · cited by 2
- MeasureTheory.Measure.singularPart_smul_rightproof · cited by 2