Theorems · Theorem · measure theory
MeasureTheory.Measure.pi_pi_aux
∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
(μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)] (s : (i : ι) → Set (α i)),
(∀ (i : ι), MeasurableSet (s i)) → (MeasureTheory.Measure.pi μ) (Set.univ.pi s) = ∏ i, (μ i) (s i)- Defined in
- Mathlib.MeasureTheory.Constructions.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Fintypestatement and proof · cited by 7,736
- Set.univstatement and proof · cited by 3,945
- Finset.univstatement and proof · cited by 3,473
- MeasurableSetstatement and proof · cited by 3,075
- Set.Nonemptyproof · cited by 2,627
- Finset.prodstatement and proof · cited by 2,356
- le_antisymmproof · cited by 2,068
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.pi_eq_generateFromproof · cited by 2