Theorems · Theorem · functional analysis
gauge_nonneg
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} (x : E), 0 ≤ gauge s xThe gauge is always nonnegative.
- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 119 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.
Cites8
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.ofPredproof · cited by 6,101
- LT.lt.leproof · cited by 2,189
- gaugestatement · cited by 85
- Real.sInf_nonnegproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- gauge_posproof · cited by 4
- gauge_gaugeRescale'proof · cited by 2
- separate_convex_open_setproof · cited by 2
- Convex.setOfPred_gauge_leproof · cited by 2
- bernsteinApproximation_uniformproof · cited by 1
- tendsto_gauge_nhds_zero_nhdsGEproof · cited by 1
- mul_gauge_le_normproof · cited by 0
- gaugeRescale_gaugeRescaleproof · cited by 0