Theorems · Theorem · sequences and series

tsum_ite_eq

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] (b : β)
  [inst_2 : DecidablePred fun x => x = b] (a : β → α)
  (L : optParam (SummationFilter β) (SummationFilter.unconditional β)) [L.LeAtTop],
  (∑'[L] (b' : β), if b' = b then a b' else 0) = a b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

8 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceDecidablePredSummationFilter.LeAtTop