Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_pos
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν],
μ.AbsolutelyContinuous ν → ∀ᵐ (x : α) ∂μ, 0 < μ.rnDeriv ν x- Cited by
- 9 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.ae_of_allproof · cited by 137
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.Measure.withDensity_rnDeriv_eqproof · cited by 31
- Ne.posproof · cited by 17
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.llr_smul_rightproof · cited by 3
- MeasureTheory.llr_smul_leftproof · cited by 2
- MeasureTheory.llr_tilted_leftproof · cited by 2
- MeasureTheory.llr_tilted_rightproof · cited by 2
- MeasureTheory.Measure.rnDeriv_div_rnDeriv_eq_div_rnDeriv_addproof · cited by 1
- MeasureTheory.exp_llr_of_acproof · cited by 1
- MeasureTheory.Measure.inv_rnDeriv_auxproof · cited by 1
- MeasureTheory.Measure.rnDeriv_pos'proof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_posproof · cited by 1