Theorems · Definition · functional analysis
gauge
{E : Type u_2} → [inst : AddCommGroup E] → [Module ℝ E] → Set E → E → ℝThe Minkowski functional. Given a set s in a real vector space, gauge s is the functional
which sends x : E to the smallest r : ℝ such that x is in s scaled by r.
- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 114 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.
Cites6
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
- InfSet.sInfproof · cited by 935
Cited by87
Results whose statement or proof uses this declaration.
- gaugeRescaleproof · cited by 12
- gauge_def'statement · cited by 8
- gauge_le_of_memstatement and proof · cited by 8
- gauge_nonnegstatement · cited by 8
- gauge_smul_of_nonnegstatement and proof · cited by 7
- gauge_zerostatement · cited by 7
- exists_lt_of_gauge_ltstatement and proof · cited by 6
- gaugeSeminormproof · cited by 6
- interior_subset_gauge_lt_onestatement · cited by 5
- setOfPred_gauge_lt_one_subset_selfstatement and proof · cited by 5
- gaugeRescale_zeroproof · cited by 4
- gauge_add_lestatement and proof · cited by 4