Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_eq_one_iff_eq
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν]
[MeasureTheory.SigmaFinite ν], μ.AbsolutelyContinuous ν → (μ.rnDeriv ν =ᵐ[ν] 1 ↔ μ = ν)- Cited by
- 2 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
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- 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
- MeasureTheory.withDensity_congr_aeproof · cited by 19
- MeasureTheory.withDensity_oneproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.rnDeriv_eq_one_iff_eqproof · cited by 1
- InformationTheory.klDiv_eq_zero_iffproof · cited by 0