Theorems · Theorem · sequences and series

HasSum.of_sigma

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommGroup α] [inst_1 : UniformSpace α] [IsUniformAddGroup α]
  {γ : β → Type u_4} {f : (b : β) × γ b → α} {g : β → α} {a : α},
  (∀ (b : β), HasSum (fun c => f ⟨b, c⟩) (g b)) → HasSum g a → (CauchySeq fun s => ∑ i ∈ s, f i) → HasSum f a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupUniformSpaceIsUniformAddGroup