Theorems · Theorem · functional analysis
gauge_ball
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {r : ℝ},
0 ≤ r → ∀ (x : E), gauge (Metric.ball 0 r) x = ‖x‖ / r- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- Metric.ballstatement and proof · cited by 735
- smul_eq_mulproof · cited by 357
- abs_of_nonnegproof · cited by 279
- div_zeroproof · cited by 251
- LE.le.eq_or_ltproof · cited by 220
Cited by3
Results whose statement or proof uses this declaration.
- gauge_closedBallproof · cited by 1
- Convex.lipschitzWith_gaugeproof · cited by 1
- mul_gauge_le_normproof · cited by 0