Theorems · Theorem · probability
ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self
∀ {Ω : Type u_2} {m m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : StandardBorelSpace Ω] (hm : m ≤ m0)
[hμ : MeasureTheory.IsFiniteMeasure μ] {t : Set Ω},
MeasurableSet t →
ProbabilityTheory.CondIndepSet m hm t t μ →
∀ᵐ (ω : Ω) ∂μ, μ[t.indicator fun ω => 1 | m] ω = 0 ∨ μ[t.indicator fun ω => 1 | m] ω = 1- Defined in
- Mathlib.Probability.Independence.ZeroOne
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Set.indicatorstatement and proof · cited by 723
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBotproof · cited by 0
- ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTopproof · cited by 0