Theorems · Theorem · probability
ProbabilityTheory.iIndepSets.meas_biInter
∀ {Ω : Type u_1} {ι : Type u_2} {π : ι → Set (Set Ω)} {x : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω},
ProbabilityTheory.iIndepSets π μ →
∀ (s : Finset ι) {f : ι → Set Ω}, (∀ i ∈ s, f i ∈ π i) → μ (⋂ i ∈ s, f i) = ∏ i ∈ s, μ (f i)- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Finset.prodstatement · cited by 2,356
- Set.iInterstatement · cited by 1,084
- ProbabilityTheory.iIndepSetsstatement and proof · cited by 18
- ProbabilityTheory.iIndepSets_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepSets.meas_iInterproof · cited by 0