Theorems · Theorem · measure theory
MeasureTheory.piContent_eq_measure_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)] [inst : Fintype ι] {s : Set ((i : ι) → X i)},
MeasurableSet s → (MeasureTheory.piContent μ) s = (MeasureTheory.Measure.pi μ) s- Defined in
- Mathlib.Probability.ProductMeasure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Set.preimageproof · cited by 4,946
- Finset.univproof · cited by 3,473
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.mapproof · cited by 858
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.piContent_tendsto_zeroproof · cited by 1