Theorems · Theorem · measure theory
Real.volume_Ioc
∀ {a b : ℝ}, MeasureTheory.volume (Set.Ioc a b) = ENNReal.ofReal (b - a)- Cited by
- 11 results in Mathlib
- Foundations
- Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.Iocstatement and proof · cited by 971
- ENNReal.ofRealstatement and proof · cited by 863
- StieltjesFunction.idproof · cited by 8
- StieltjesFunction.measure_Iocproof · cited by 8
- Real.volume_valproof · cited by 4
- StieltjesFunction.id_applyproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_constproof · cited by 33
- AddCircle.volume_closedBallproof · cited by 4
- BoxIntegral.unitPartition.volume_boxproof · cited by 2
- Real.volume_real_Iocproof · cited by 2
- Real.volume_uIocproof · cited by 2
- MeasureTheory.LevyProkhorov.continuous_toMeasure_probabilityMeasureproof · cited by 1
- intervalIntegral.norm_integral_le_of_norm_le_const_aeproof · cited by 1
- unitInterval.volume_Ioiproof · cited by 0
- unitInterval.volume_uIocproof · cited by 0
- unitInterval.volume_Iocproof · cited by 0