Theorems · Theorem · measure theory
Real.volume_Icc_pi
∀ {ι : Type u_1} [inst : Fintype ι] {a b : ι → ℝ}, MeasureTheory.volume (Set.Icc a b) = ∏ i, ENNReal.ofReal (b i - a i)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 246 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.
Cites15
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
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Set.Iccstatement and proof · cited by 1,702
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
- Finset.prod_congrproof · cited by 646
Cited by5
Results whose statement or proof uses this declaration.
- Real.volume_pi_Iooproof · cited by 1
- Real.volume_Icc_pi_toRealproof · cited by 1
- Real.volume_pi_Icoproof · cited by 1
- MeasureTheory.integral_divergence_of_hasFDerivAt_off_countableproof · cited by 1
- Real.volume_pi_Iocproof · cited by 1