Theorems · Theorem · sequences and series

summable_sum_mul_antidiagonal_of_summable_mul

∀ {α : Type u_3} {A : Type u_4} [inst : AddCommMonoid A] [inst_1 : Finset.HasAntidiagonal A]
  [inst_2 : TopologicalSpace α] [inst_3 : NonUnitalNonAssocSemiring α] {f g : A → α} [T3Space α]
  [IsTopologicalSemiring α],
  (Summable fun x => f x.1 * g x.2) → Summable fun n => ∑ kl ∈ Finset.HasAntidiagonal.antidiagonal n, f kl.1 * g kl.2

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

3 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidFinset.HasAntidiagonalTopologicalSpaceNonUnitalNonAssocSemiringT3SpaceIsTopologicalSemiring