Theorems · Theorem · measure theory
MeasureTheory.Measure.setLIntegral_rnDeriv
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν]
[MeasureTheory.SFinite ν], μ.AbsolutelyContinuous ν → ∀ (s : Set α), ∫⁻ (x : α) in s, μ.rnDeriv ν x ∂ν = μ s- Cited by
- 6 results in Mathlib
- Foundations
- Depth 215 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.withDensity_rnDeriv_eqproof · cited by 31
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.setLIntegral_rnDerivAuxproof · cited by 2
- MeasurableEmbedding.rnDeriv_map_auxproof · cited by 1
- ProbabilityTheory.posterior_eq_withDensityproof · cited by 1
- MeasureTheory.lintegral_rnDeriv_compProdproof · cited by 1
- MeasureTheory.MeasurePreserving.rnDeriv_comp_aeEqproof · cited by 1
- Ergodic.eq_smul_of_absolutelyContinuousproof · cited by 1