Theorems · Theorem · functional analysis
gauge_of_subset_zero
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E}, s ⊆ 0 → gauge s = 0- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 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.
Cites9
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.zerostatement · cited by 87
- gaugestatement · cited by 85
- Set.subset_singleton_iff_eqproof · cited by 10
- gauge_emptyproof · cited by 2
- gauge_zero'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- gauge_smul_left_of_nonnegproof · cited by 1