Theorems · Theorem · measure theory
MeasureTheory.volume_pi_pi
∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasureTheory.MeasureSpace (α i)]
[∀ (i : ι), MeasureTheory.SigmaFinite MeasureTheory.volume] (s : (i : ι) → Set (α i)),
MeasureTheory.volume (Set.univ.pi s) = ∏ i, MeasureTheory.volume (s i)- Defined in
- Mathlib.MeasureTheory.Constructions.Pi
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Set.univstatement · cited by 3,945
- Finset.univstatement · cited by 3,473
- Finset.prodstatement · cited by 2,356
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- Set.pistatement · cited by 405
- MeasureTheory.MeasureSpacestatement and proof · cited by 51
Cited by5
Results whose statement or proof uses this declaration.
- Real.volume_Icc_piproof · cited by 5
- MeasureTheory.addHaarMeasure_eq_volume_piproof · cited by 3
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- Real.smul_map_diagonal_volume_piproof · cited by 1
- Real.volume_pi_le_prod_diamproof · cited by 1