Theorems · Theorem · sequences and series

HasProd.of_sigma

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Constructions

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommGroupUniformSpaceIsUniformGroup