Theorems · Theorem · probability
MeasureTheory.Measure.infinitePi_map_eval_prod
∀ {ι : Type u_1} {Ω : ι → Type u_4} {mΩ : (i : ι) → MeasurableSpace (Ω i)} {P : (i : ι) → MeasureTheory.Measure (Ω i)}
[∀ (i : ι), MeasureTheory.IsProbabilityMeasure (P i)] {i j : ι},
i ≠ j → MeasureTheory.Measure.map (fun ω => (ω i, ω j)) (MeasureTheory.Measure.infinitePi P) = (P i).prod (P j)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- MeasureTheory.Measure.mapstatement · cited by 858
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.Measure.prodstatement and proof · cited by 353
- Measurable.aemeasurableproof · cited by 304
- measurable_id'proof · cited by 145
- measurable_pi_applyproof · cited by 77
- MeasureTheory.Measure.infinitePistatement · cited by 48
- ProbabilityTheory.IndepFun.map_prod_eq_prod_map_mapproof · cited by 5
- MeasureTheory.Measure.infinitePi_map_evalproof · cited by 4
- ProbabilityTheory.iIndepFun.indepFunproof · cited by 3
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