Theorems · Theorem · functional analysis
gauge_lt_one_subset_self
Deprecated since 2026-06-17Use setOfPred_gauge_lt_one_subset_self instead.
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E},
Convex ℝ s → 0 ∈ s → Absorbent ℝ s → {x | gauge s x < 1} ⊆ sAlias of setOfPred_gauge_lt_one_subset_self.
- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Modulestatement · cited by 20,661
- AddCommGroupstatement · cited by 12,871
- Set.ofPredstatement · cited by 6,101
- Convexstatement · cited by 551
- gaugestatement · cited by 85
- Absorbentstatement · cited by 60
- setOfPred_gauge_lt_one_subset_selfproof · cited by 5
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