Theorems · Theorem · measure theory
MeasureTheory.isSigmaSubadditive_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.piContent μ).IsSigmaSubadditiveThe projectiveFamilyContent associated to a family of probability measures is
σ-subadditive.
- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 277 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.iUnionproof · cited by 2,483
- Disjointproof · cited by 2,201
- Function.onFunproof · cited by 570
- Pairwiseproof · cited by 516
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.measurableCylindersstatement and proof · cited by 48
- MeasureTheory.AddContent.IsSigmaSubadditivestatement · cited by 11
- MeasureTheory.piContentstatement and proof · cited by 8
- MeasureTheory.isSetRing_measurableCylindersproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.infinitePiproof · cited by 48
- MeasureTheory.Measure.isProjectiveLimit_infinitePiproof · cited by 3