Theorems · Definition · measure theory
MeasureTheory.piContent
{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)] →
MeasureTheory.AddContent ENNReal (MeasureTheory.measurableCylinders X)Consider a family of probability measures. You can take their products for any finite subfamily. This gives an additive content on the measurable cylinders.
- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ENNRealstatement · cited by 9,879
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.AddContentstatement · cited by 78
- MeasureTheory.measurableCylindersstatement · cited by 48
- MeasureTheory.projectiveFamilyContentproof · cited by 11
- MeasureTheory.isProjectiveMeasureFamily_piproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.infinitePiproof · cited by 48
- MeasureTheory.piContent_cylinderstatement · cited by 5
- MeasureTheory.Measure.isProjectiveLimit_infinitePiproof · cited by 3
- MeasureTheory.piContent_eq_measure_pistatement and proof · cited by 1
- MeasureTheory.piContent_tendsto_zerostatement and proof · cited by 1
- MeasureTheory.isSigmaSubadditive_piContentstatement and proof · cited by 1
- MeasureTheory.Measure.infinitePiNat_map_piCongrLeftstatement and proof · cited by 1
- MeasureTheory.Measure.piContent_eq_infinitePiNatstatement · cited by 0
- MeasureTheory.piContent.congr_simpstatement and proof · cited by 0