Theorems · Theorem · Lie groups

tendsto_multiset_prod

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

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommMonoidContinuousMul