Theorems · Theorem · functional analysis
gauge_unit_ball
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (x : E), gauge (Metric.ball 0 1) x = ‖x‖- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Metric.ballstatement · cited by 735
- gaugestatement and proof · cited by 85
- normSeminormproof · cited by 32
- ball_normSeminormproof · cited by 7
- Seminorm.gauge_ballproof · cited by 2
- coe_normSeminormproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- gauge_ballproof · cited by 3