Theorems · Theorem · order theory

Filter.Tendsto.atBot_of_mul_isBoundedUnder_ge

∀ {α : Type u_1} {M : Type u_2} [inst : CommMonoid M] [inst_1 : Preorder M] [IsOrderedCancelMonoid M] {l : Filter α}
  {f g : α → M},
  Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) l g →
    Filter.Tendsto (fun x => f x * g x) l Filter.atBot → Filter.Tendsto f l Filter.atBot

Defined in

Mathlib.Order.Filter.AtTopBot.Monoid

Cited by

0 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Quot.sound

Assumes

CommMonoidPreorderIsOrderedCancelMonoid