Theorems · Theorem · probability
ProbabilityTheory.IndepFun_iff_Indep
∀ {Ω : Type u_1} {β : Type u_3} {γ : Type u_4} {x : MeasurableSpace Ω} [mβ : MeasurableSpace β] [mγ : MeasurableSpace γ]
(f : Ω → β) (g : Ω → γ) (μ : MeasureTheory.Measure Ω),
ProbabilityTheory.IndepFun f g μ ↔ ProbabilityTheory.Indep (MeasurableSpace.comap f mβ) (MeasurableSpace.comap g mγ) μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.diracproof · cited by 210
- ProbabilityTheory.IndepFunstatement · cited by 192
- MeasurableSpace.comapstatement and proof · cited by 124
- ProbabilityTheory.Kernel.constproof · cited by 93
- ProbabilityTheory.Indepstatement · cited by 43
- ProbabilityTheory.Kernel.Indepproof · cited by 42
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun_iffproof · cited by 2