Theorems · Theorem · measure theory
Real.volume_closedBall
∀ (a r : ℝ), MeasureTheory.volume (Metric.closedBall a r) = ENNReal.ofReal (2 * r)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 246 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 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
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
- Metric.closedBallstatement · cited by 704
- two_mulproof · cited by 232
- add_sub_cancel_leftproof · cited by 198
- sub_addproof · cited by 51
- Real.volume_Iccproof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- AddCircle.volume_closedBallproof · cited by 4
- Real.volume_closedEBallproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- Real.volume_pi_closedBallproof · cited by 0
- Real.volume_real_closedBallproof · cited by 0