Theorems · Theorem · probability
ProbabilityTheory.iIndepSets_iff
∀ {Ω : Type u_1} {ι : Type u_2} {x : MeasurableSpace Ω} (π : ι → Set (Set 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 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Filter.Eventuallyproof · cited by 3,134
- Finset.prodstatement and proof · cited by 2,356
- Set.iInterstatement and proof · cited by 1,084
- MeasureTheory.ae_dirac_eqproof · cited by 31
- ProbabilityTheory.iIndepSetsstatement · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepSets.meas_biInterproof · cited by 1