Theorems · Theorem · measure theory
MeasureTheory.Measure.withDensity_rnDeriv_eq
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [μ.HaveLebesgueDecomposition ν],
μ.AbsolutelyContinuous ν → ν.withDensity (μ.rnDeriv ν) = μ- Cited by
- 31 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- zero_addproof · cited by 2,366
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- 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.singularPartproof · cited by 71
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.singularPart_eq_zeroproof · cited by 1
Cited by31
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_posproof · cited by 9
- MeasureTheory.map_eq_withDensity_pdfproof · cited by 6
- MeasureTheory.Measure.setLIntegral_rnDerivproof · cited by 6
- MeasureTheory.integral_rnDeriv_smulproof · cited by 5
- MeasureTheory.integrable_rnDeriv_smul_iffproof · cited by 4
- MeasureTheory.mconv_eq_withDensity_mlconvolution_rnDerivproof · cited by 3
- MeasureTheory.conv_eq_withDensity_lconvolution_rnDerivproof · cited by 3
- MeasureTheory.Measure.setIntegral_toReal_rnDerivproof · cited by 3
- MeasureTheory.Measure.setLIntegral_rnDeriv'proof · cited by 2
- MeasureTheory.Measure.rnDeriv_eq_one_iff_eqproof · cited by 2
- MeasureTheory.Measure.rnDeriv_mul_rnDerivproof · cited by 2
- ProbabilityTheory.Kernel.setLIntegral_rnDerivproof · cited by 2