Theorems · Theorem · functional analysis
gauge_closedBall
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {r : ℝ},
0 ≤ r → ∀ (x : E), gauge (Metric.closedBall 0 r) x = ‖x‖ / r- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- nhdsWithinproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
Cited by1
Results whose statement or proof uses this declaration.
- le_gauge_of_subset_closedBallproof · cited by 0