Theorems · Theorem · measure theory
Real.volume_Ioo
∀ {a b : ℝ}, MeasureTheory.volume (Set.Ioo a b) = ENNReal.ofReal (b - a)- Cited by
- 17 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.
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 · 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.Ioostatement and proof · cited by 1,214
- ENNReal.ofRealstatement and proof · cited by 863
- StieltjesFunction.idproof · cited by 8
- StieltjesFunction.id_leftLimproof · cited by 4
- Real.volume_valproof · cited by 4
- StieltjesFunction.id_applyproof · cited by 4
Cited by17
Results whose statement or proof uses this declaration.
- Real.volume_ballproof · cited by 6
- Real.volume_Ioiproof · cited by 4
- MeasureTheory.exists_null_frontier_thickeningproof · cited by 3
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- Real.smul_map_volume_mul_leftproof · cited by 2
- NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integralproof · cited by 1
- Real.volume_real_Iooproof · cited by 1
- volume_regionBetween_eq_lintegral'proof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT'_volumeproof · cited by 1
- Real.volume_Iioproof · cited by 1
- norm_sub_le_mul_volume_of_norm_deriv_le_of_leproof · cited by 1