Theorems · Theorem · probability
ProbabilityTheory.iIndepSets.meas_iInter
∀ {Ω : Type u_1} {ι : Type u_2} {π : ι → Set (Set Ω)} {x : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω}
{s : ι → Set Ω} [inst : Fintype ι],
ProbabilityTheory.iIndepSets π μ → (∀ (i : ι), s i ∈ π i) → μ (⋂ i, s i) = ∏ i, μ (s i)- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites14
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
- Finsetproof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement · cited by 2,356
- Set.iInterstatement and proof · cited by 1,084
- Set.iInter_congr_Propproof · cited by 170
- ProbabilityTheory.iIndepSetsstatement and proof · cited by 18
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