Theorems · Theorem · measure theory
MeasureTheory.Measure.withDensity_rnDeriv_le
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α), ν.withDensity (μ.rnDeriv ν) ≤ μ- Cited by
- 9 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.
Cites13
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
- ENNRealproof · cited by 9,879
- le_rflproof · cited by 1,558
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionproof · cited by 92
- MeasureTheory.Measure.singularPartproof · cited by 71
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.le_add_leftproof · cited by 14
- MeasureTheory.Measure.zero_leproof · cited by 5
- MeasureTheory.Measure.rnDeriv_defproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.setLIntegral_rnDeriv_leproof · cited by 3
- ProbabilityTheory.Kernel.setLIntegral_rnDeriv_leproof · cited by 1
- MeasureTheory.withDensity_pdf_le_mapproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_leftproof · cited by 1
- AEMeasurable.withDensity_rnDerivproof · cited by 0
- MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDeriv_swapproof · cited by 0
- MeasureTheory.Measure.mutuallySingular_compProd_iffproof · cited by 0
- MeasureTheory.Measure.mutuallySingular_compProd_left_iffproof · cited by 0
- MeasureTheory.Measure.setIntegral_toReal_rnDeriv_leproof · cited by 0