Theorems · Theorem · probability
ProbabilityTheory.Kernel.measurableSet_mutuallySingularSetSlice
∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
[hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] (κ η : ProbabilityTheory.Kernel α γ) (a : α),
MeasurableSet (κ.mutuallySingularSetSlice η a)- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MeasurableSetstatement · cited by 3,075
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- measurable_prodMk_leftproof · cited by 69
- ProbabilityTheory.Kernel.mutuallySingularSetSlicestatement · cited by 19
- ProbabilityTheory.Kernel.measurableSet_mutuallySingularSetproof · cited by 4
- ProbabilityTheory.Kernel.mutuallySingularSetproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.rnDeriv_add_singularPartproof · cited by 7
- ProbabilityTheory.Kernel.mutuallySingular_singularPartproof · cited by 6
- ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zeroproof · cited by 1
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_apply_eq_zeroproof · cited by 1
- ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_measure_eq_zeroproof · cited by 1
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_measure_eq_zeroproof · cited by 0