Theorems · Theorem · functional analysis

gauge_smul_left

∀ {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 : Module α E] [SMulCommClass α ℝ ℝ] [IsScalarTower α ℝ ℝ] [IsScalarTower α ℝ E] {s : Set E},
  (∀ x ∈ s, -x ∈ s) → ∀ (a : α), gauge (a • s) = |a|⁻¹ • gauge s

Defined in

Mathlib.Analysis.Convex.Gauge

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupModuleFieldLinearOrderIsStrictOrderedRingMulActionWithZeroIsStrictOrderedModuleModuleSMulCommClassIsScalarTowerIsScalarTower