Theorems · Theorem · measure theory
Real.volume_ball
∀ (a r : ℝ), MeasureTheory.volume (Metric.ball a r) = ENNReal.ofReal (2 * r)
- Cited by
- 6 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.ballstatement · cited by 735
- two_mulproof · cited by 232
- add_sub_cancel_leftproof · cited by 198
- sub_addproof · cited by 51
- Real.volume_Iooproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.convexBodyLT_volumeproof · cited by 2
- volume_iUnion_setOfPred_liouvilleWithproof · cited by 2
- Real.volume_eballproof · cited by 1
- NumberField.mixedEmbedding.convexBodyLT'_volumeproof · cited by 1
- Real.volume_pi_ballproof · cited by 1
- Real.volume_real_ballproof · cited by 0