Theorems · Theorem · functional analysis

Filter.isBoundedUnder_le_mul_tendsto_zero

∀ {α : Type u_1} {ι : Type u_3} [inst : NonUnitalSeminormedRing α] {f g : ι → α} {l : Filter ι},
  Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l (norm ∘ f) →
    Filter.Tendsto g l (nhds 0) → Filter.Tendsto (fun x => f x * g x) l (nhds 0)

Defined in

Mathlib.Analysis.Normed.Ring.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalSeminormedRing