Theorems · Theorem · measure theory
Real.volume_Icc
∀ {a b : ℝ}, MeasureTheory.volume (Set.Icc a b) = ENNReal.ofReal (b - a)- Cited by
- 18 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
- Set.Iccstatement and proof · cited by 1,702
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
- StieltjesFunction.measure_Iccproof · cited by 8
- StieltjesFunction.idproof · cited by 8
- StieltjesFunction.id_leftLimproof · cited by 4
- Real.volume_valproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- Real.volume_Icc_piproof · cited by 5
- Real.volume_closedBallproof · cited by 5
- MeasureTheory.addHaarMeasure_eq_volume_piproof · cited by 3
- Real.volume_real_Iccproof · cited by 2
- Real.volume_univproof · cited by 2
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Icoproof · cited by 1
- lintegral_fderiv_lineMap_eq_edistproof · cited by 1
- LocallyIntegrable.ae_hasDerivAt_integralproof · cited by 1
- MeasureTheory.hausdorffMeasure_affineSegmentproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- StieltjesFunction.ae_hasDerivAtproof · cited by 1
- Real.volume_intervalproof · cited by 1