Theorems · Theorem · sequences and series

HasSum.mul

∀ {ι : Type u_1} {κ : Type u_2} {α : Type u_3} [inst : TopologicalSpace α] [T3Space α]
  [inst_2 : NonUnitalNonAssocSemiring α] [IsTopologicalSemiring α] {f : ι → α} {g : κ → α} {s t : α},
  HasSum f s → HasSum g t → (Summable fun x => f x.1 * g x.2) → HasSum (fun x => f x.1 * g x.2) (s * t)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

3 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT3SpaceNonUnitalNonAssocSemiringIsTopologicalSemiring