Theorems · Theorem · sequences and series

tsum_apply

∀ {α : Type u_1} {ι : Type u_4} {X : α → Type u_5} [inst : (x : α) → AddCommMonoid (X x)]
  [inst_1 : (x : α) → TopologicalSpace (X x)] {L : SummationFilter ι} [L.NeBot] [∀ (x : α), T2Space (X x)]
  {f : ι → (x : α) → X x} {x : α}, Summable f L → (∑'[L] (i : ι), f i) x = ∑'[L] (i : ι), f i x

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Constructions

Cited by

5 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceSummationFilter.NeBotT2Space