Theorems · Theorem · probability
ProbabilityTheory.lintegral_prod_eq_prod_lintegral_of_indepFun
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {ι : Type u_3} (s : Finset ι)
(X : ι → Ω → ENNReal),
ProbabilityTheory.iIndepFun X μ →
(∀ (i : ι), Measurable (X i)) → ∫⁻ (ω : Ω), ∏ i ∈ s, X i ω ∂μ = ∏ i ∈ s, ∫⁻ (ω : Ω), X i ω ∂μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- mul_oneproof · cited by 3,885
- Finset.prodstatement and proof · cited by 2,356
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.IsProbabilityMeasureproof · cited by 392
- Measurable.aemeasurableproof · cited by 304
- Finset.consproof · cited by 221
- ProbabilityTheory.iIndepFunstatement and proof · cited by 138
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