Theorems · Theorem · functional analysis
setOfPred_gauge_lt_one_subset_self
∀ {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} ⊆ s- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 5 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.
Cites11
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
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement and proof · cited by 6,101
- Convexstatement and proof · cited by 551
- openSegmentproof · cited by 102
- gaugestatement and proof · cited by 85
- Absorbentstatement and proof · cited by 60
- Convex.openSegment_subsetproof · cited by 3
- mem_openSegment_of_gauge_lt_oneproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- setOfPred_gauge_lt_one_eq_self_of_isOpenproof · cited by 4
- mem_closure_of_gauge_le_oneproof · cited by 3
- bernsteinApproximation_uniformproof · cited by 1
- setOf_gauge_lt_one_subset_selfproof · cited by 0
- gauge_lt_one_subset_selfproof · cited by 0