Theorems · Theorem · probability
ProbabilityTheory.Kernel.indepSet_iff_indepSets_singleton
∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {s t : Set Ω} {m0 : MeasurableSpace Ω},
MeasurableSet s →
MeasurableSet t →
∀ (κ : ProbabilityTheory.Kernel α Ω) (μ : MeasureTheory.Measure α) [ProbabilityTheory.IsZeroOrMarkovKernel κ],
ProbabilityTheory.Kernel.IndepSet s t κ μ ↔ ProbabilityTheory.Kernel.IndepSets {s} {t} κ μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 196 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.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- Set.mem_singleton_iffproof · cited by 172
- MeasurableSpace.generateFrom_leproof · cited by 49
- ProbabilityTheory.IsZeroOrMarkovKernelstatement and proof · cited by 32
- ProbabilityTheory.Kernel.IndepSetsstatement and proof · cited by 27
- ProbabilityTheory.Kernel.IndepSetstatement · cited by 18
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- ProbabilityTheory.Kernel.Indep.indepSetsproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.indepSet_iff_measure_inter_eq_mulproof · cited by 2
- ProbabilityTheory.indepSet_iff_indepSets_singletonproof · cited by 1
- ProbabilityTheory.condIndepSet_iff_condIndepSets_singletonproof · cited by 1