Theorems · Theorem · measure theory
MeasureTheory.Measure.infinitePi_pi_of_countable
∀ {ι : Type u_1} {X : ι → Type u_2} {mX : (i : ι) → MeasurableSpace (X i)} (μ : (i : ι) → MeasureTheory.Measure (X i))
[hμ : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] {s : Set ι},
Countable ↑s →
∀ {t : (i : ι) → Set (X i)},
(∀ i ∈ s, MeasurableSet (t i)) → (MeasureTheory.Measure.infinitePi μ) (s.pi t) = ∏' (i : ↑s), (μ ↑i) (t ↑i)- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites52
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 and proof · cited by 9,879
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.infinitePi_pi_univproof · cited by 1