Theorems · Theorem · measure theory
Real.volume_pi_Ioc_toReal
∀ {ι : Type u_1} [inst : Fintype ι] {a b : ι → ℝ},
a ≤ b → (MeasureTheory.volume (Set.univ.pi fun i => Set.Ioc (a i) (b i))).toReal = ∏ i, (b i - a i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 248 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.
Cites19
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 and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.Iocstatement · cited by 971
- ENNReal.ofRealproof · cited by 863
Cited by3
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.volume_applyproof · cited by 3
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- BoxIntegral.Box.volume_apply'proof · cited by 0