Theorems · Theorem · measure theory
MeasureTheory.Measure.singularPart_le
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α), μ.singularPart ν ≤ μ- Cited by
- 7 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- le_rflproof · cited by 1,558
- MeasureTheory.Measure.withDensityproof · cited by 265
- MeasureTheory.Measure.rnDerivproof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionproof · cited by 92
- MeasureTheory.Measure.singularPartstatement and proof · cited by 71
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.le_add_rightproof · cited by 12
- MeasureTheory.Measure.zero_leproof · cited by 5
- MeasureTheory.Measure.singularPart_defproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.singularPart_eq_zero_of_acproof · cited by 4
- MeasureTheory.Measure.MutuallySingular.singularPartproof · cited by 2
- MeasureTheory.SignedMeasure.singularPart_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_leftproof · cited by 1
- MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPartproof · cited by 1
- MeasureTheory.Measure.integral_toReal_rnDeriv'proof · cited by 0
- AEMeasurable.singularPartproof · cited by 0