Theorems · Theorem · commutative algebra

seminormFromBounded_eq_zero_iff

∀ {R : Type u_1} [inst : CommRing R] {f : R → ℝ} {c : ℝ},
  0 ≤ f → (∀ (x y : R), f (x * y) ≤ c * f x * f y) → ∀ (x : R), seminormFromBounded' f x = 0 ↔ f x = 0

If f : R → ℝ is a nonnegative, multiplicatively bounded function, then seminormFromBounded' f x = 0 if and only if f x = 0.

Defined in

Mathlib.Analysis.Normed.Unbundled.SeminormFromBounded

Cited by

4 results in Mathlib

Foundations

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

Assumes

CommRing