Theorems · Theorem · sequences and series

summable_sum_mul_range_of_summable_mul

∀ {α : Type u_3} [inst : TopologicalSpace α] [inst_1 : NonUnitalNonAssocSemiring α] {f g : ℕ → α} [T3Space α]
  [IsTopologicalSemiring α],
  (Summable fun x => f x.1 * g x.2) → Summable fun n => ∑ k ∈ Finset.range (n + 1), f k * g (n - k)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNonUnitalNonAssocSemiringT3SpaceIsTopologicalSemiring