Theorems · Theorem · probability
ProbabilityTheory.Kernel.rnDeriv_eq_rnDeriv_measure
∀ {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 η]
[ProbabilityTheory.IsFiniteKernel κ] {a : α}, κ.rnDeriv η a =ᵐ[η a] (κ a).rnDeriv (η a)- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 333 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.rnDerivstatement · cited by 234
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- ProbabilityTheory.Kernel.rnDerivstatement · cited by 45
- ProbabilityTheory.Kernel.measurable_rnDerivproof · cited by 11
Cited by13
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.setLIntegral_rnDerivproof · cited by 2
- ProbabilityTheory.posterior_eq_withDensity_of_countableproof · cited by 2
- ProbabilityTheory.Kernel.setLIntegral_rnDeriv_leproof · cited by 1
- ProbabilityTheory.Kernel.withDensity_rnDeriv_eqproof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_eq_one_iff_eqproof · cited by 1
- ProbabilityTheory.posterior_eq_withDensityproof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_lt_topproof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_posproof · cited by 1
- ProbabilityTheory.Kernel.eq_rnDerivproof · cited by 0
- ProbabilityTheory.Kernel.rnDeriv_addproof · cited by 0
- ProbabilityTheory.Kernel.rnDeriv_selfproof · cited by 0
- ProbabilityTheory.Kernel.rnDeriv_singularPartproof · cited by 0