Theorems · Theorem · functional analysis
le_gauge_of_subset_closedBall
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {s : Set E} {r : ℝ} {x : E},
Absorbent ℝ s → 0 ≤ r → s ⊆ Metric.closedBall 0 r → ‖x‖ / r ≤ gauge s x- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement · cited by 5,413
- Metric.closedBallstatement and proof · cited by 704
- gaugestatement and proof · cited by 85
- Absorbentstatement and proof · cited by 60
- gauge_monoproof · cited by 4
- gauge_closedBallproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.