Theorems · Theorem · sequences and series

HasSum.prod_fiberwise

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] [ContinuousAdd α]
  [RegularSpace α] {f : β × γ → α} {g : β → α} {a : α},
  HasSum f a → (∀ (b : β), HasSum (fun c => f (b, c)) (g b)) → HasSum g a

If a series f on β × γ has sum a and for each b the restriction of f to {b} × γ has sum g b, then the series g has sum a.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Constructions

Cited by

7 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceContinuousAddRegularSpace