Theorems · Theorem · measure theory
EuclideanSpace.volume_closedBall_fin_three
∀ (x : EuclideanSpace ℝ (Fin 3)) (r : ℝ), MeasureTheory.volume (Metric.closedBall x r) = ENNReal.ofReal r ^ 3 * ENNReal.ofReal (Real.pi * 4 / 3)
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- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
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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 and proof · cited by 9,879
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
- Metric.closedBallstatement · cited by 704
- EuclideanSpacestatement and proof · cited by 307
- MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ballproof · cited by 9
- EuclideanSpace.volume_ball_fin_threeproof · cited by 1
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