Theorems · Theorem · probability
ProbabilityTheory.indep_iSup_of_directed_le
∀ {Ω : Type u_1} {ι : Type u_2} {m : ι → MeasurableSpace Ω} {m1 _mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω}
[MeasureTheory.IsZeroOrProbabilityMeasure μ],
(∀ (i : ι), ProbabilityTheory.Indep (m i) m1 μ) →
(∀ (i : ι), m i ≤ _mΩ) → m1 ≤ _mΩ → Directed (fun x1 x2 => x1 ≤ x2) m → ProbabilityTheory.Indep (⨆ i, m i) m1 μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- iSupstatement · cited by 2,415
- Directedstatement and proof · cited by 213
- MeasureTheory.IsZeroOrProbabilityMeasurestatement and proof · cited by 46
- ProbabilityTheory.Indepstatement and proof · cited by 43
- ProbabilityTheory.Kernel.indep_iSup_of_directed_leproof · cited by 5
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