Theorems · Theorem · measure theory
Real.volume_pi_ball
∀ {ι : Type u_1} [inst : Fintype ι] (a : ι → ℝ) {r : ℝ},
0 < r → MeasureTheory.volume (Metric.ball a r) = ENNReal.ofReal ((2 * r) ^ Fintype.card ι)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- Finset.cardproof · cited by 2,327
- LT.lt.leproof · cited by 2,189
- Fintype.cardstatement and proof · cited by 1,386
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- ENNReal.ofRealstatement and proof · cited by 863
Cited by1
Results whose statement or proof uses this declaration.
- Real.dimH_ball_piproof · cited by 2