Theorems · Theorem · measure theory
MeasureTheory.piContent_cylinder
∀ {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)] {I : Finset ι} {S : Set ((i : ↥I) → X ↑i)},
MeasurableSet S →
(MeasureTheory.piContent μ) (MeasureTheory.cylinder I S) = (MeasureTheory.Measure.pi fun i => μ ↑i) S- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.Measure.pistatement · cited by 130
- MeasureTheory.AddContentstatement · cited by 78
- MeasureTheory.cylinderstatement · cited by 49
- MeasureTheory.measurableCylindersstatement · cited by 48
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.isProjectiveLimit_infinitePiproof · cited by 3
- MeasureTheory.piContent_eq_measure_piproof · cited by 1
- MeasureTheory.piContent_tendsto_zeroproof · cited by 1
- MeasureTheory.Measure.infinitePiNat_map_piCongrLeftproof · cited by 1
- MeasureTheory.Measure.piContent_eq_infinitePiNatproof · cited by 0