Theorems · Theorem · probability
ProbabilityTheory.Kernel.withDensity_congr_ae
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (κ : ProbabilityTheory.Kernel α β)
[inst : ProbabilityTheory.IsSFiniteKernel κ] {f g : α → β → ENNReal},
Measurable (Function.uncurry f) →
Measurable (Function.uncurry g) → (∀ (a : α), f a =ᵐ[κ a] g a) → κ.withDensity f = κ.withDensity g- Defined in
- Mathlib.Probability.Kernel.WithDensity
- Cited by
- 1 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.
Cites17
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
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.withDensityproof · cited by 265
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.withDensity_sub_add_cancelproof · cited by 1