Theorems · Theorem · functional analysis

gauge_smul_of_nonneg

∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {α : Type u_3} [inst_2 : Field α]
  [inst_3 : LinearOrder α] [IsStrictOrderedRing α] [inst_5 : MulActionWithZero α ℝ] [IsStrictOrderedModule α ℝ]
  [inst_7 : MulActionWithZero α E] [IsScalarTower α ℝ (Set E)] {s : Set E} {a : α},
  0 ≤ a → ∀ (x : E), gauge s (a • x) = a • gauge s x

Defined in

Mathlib.Analysis.Convex.Gauge

Cited by

7 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupModuleFieldLinearOrderIsStrictOrderedRingMulActionWithZeroIsStrictOrderedModuleMulActionWithZeroIsScalarTower