Theorems · Theorem · functional analysis
Convex.setOfPred_gauge_le
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E},
Convex ℝ s → 0 ∈ s → Absorbent ℝ s → ∀ (a : ℝ), Convex ℝ {x | gauge s x ≤ a}- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Modulestatement and proof · cited by 20,661
- Semiringproof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- PartialOrderproof · cited by 6,410
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Convexstatement and proof · cited by 551
- gaugestatement and proof · cited by 85
- Absorbentstatement and proof · cited by 60
Cited by2
Results whose statement or proof uses this declaration.
- Convex.setOf_gauge_leproof · cited by 0
- Convex.gauge_leproof · cited by 0