Theorems · Theorem · Lie groups

tendsto_list_prod

∀ {ι : Type u_1} {α : Type u_2} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : Monoid M] [ContinuousMul M]
  {f : ι → α → M} {x : Filter α} {a : ι → M} (l : List ι),
  (∀ i ∈ l, Filter.Tendsto (f i) x (nhds (a i))) →
    Filter.Tendsto (fun b => (List.map (fun c => f c b) l).prod) x (nhds (List.map a l).prod)

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

3 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMonoidContinuousMul