Theorems · Theorem · probability
ProbabilityTheory.Kernel.withDensity_absolutelyContinuous
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
[inst : ProbabilityTheory.IsSFiniteKernel κ] (f : α → β → ENNReal) (a : α),
((κ.withDensity f) a).AbsolutelyContinuous (κ a)- Defined in
- Mathlib.Probability.Kernel.WithDensity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 211 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Measurableproof · cited by 1,499
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- zero_applyproof · cited by 251
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- ProbabilityTheory.Kernel.withDensitystatement · cited by 45
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- ProbabilityTheory.Kernel.withDensity_applyproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_absolutelyContinuousproof · cited by 2