Theorems · Theorem · probability
ProbabilityTheory.Kernel.rnDeriv_toReal_pos
∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {κ η : ProbabilityTheory.Kernel α γ}
[hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] [ProbabilityTheory.IsFiniteKernel κ]
[ProbabilityTheory.IsFiniteKernel η] {a : α},
(κ a).AbsolutelyContinuous (η a) → ∀ᵐ (x : γ) ∂κ a, 0 < (κ.rnDeriv η a x).toReal- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 336 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallystatement · cited by 3,134
- MeasureTheory.aestatement · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ENNReal.toRealstatement · cited by 859
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.