Theorems · Theorem · measure theory
MeasureTheory.Measure.infinitePi_pi
∀ {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 : Finset ι} {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
- 6 results in Mathlib
- Foundations
- Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- 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
- SetLike.coestatement and proof · cited by 8,199
- Set.univproof · cited by 3,945
- MeasurableSetstatement and proof · cited by 3,075
- Finset.prodstatement and proof · cited by 2,356
- Set.extproof · cited by 2,266
- Set.pistatement and proof · cited by 405
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.infinitePi_map_piproof · cited by 2
- MeasureTheory.Measure.infinitePi_map_piCurry_symmproof · cited by 2
- MeasureTheory.Measure.infinitePi_map_piCongrLeftproof · cited by 1
- MeasureTheory.Measure.infinitePi_map_restrict'proof · cited by 1
- MeasureTheory.Measure.infinitePi_pi_of_countableproof · cited by 1
- MeasureTheory.Measure.infinitePi_eq_piproof · cited by 0