Theorems · Theorem · measure theory
Real.volume_pi_Ioo
∀ {ι : Type u_1} [inst : Fintype ι] {a b : ι → ℝ},
MeasureTheory.volume (Set.univ.pi fun i => Set.Ioo (a i) (b i)) = ∏ i, ENNReal.ofReal (b i - a i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- 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 · cited by 1,323
- Set.Ioostatement · cited by 1,214
- ENNReal.ofRealstatement · cited by 863
Cited by1
Results whose statement or proof uses this declaration.
- Real.volume_pi_Ioo_toRealproof · cited by 0