Theorems · Theorem · sequences and series

HasSum.hasSum_symmetricIco_of_hasSum_symmetricIcc

∀ {α : Type u_1} {f : ℤ → α} [inst : AddCommGroup α] [inst_1 : TopologicalSpace α] [ContinuousAdd α] {a : α},
  HasSum f a (SummationFilter.symmetricIcc ℤ) →
    Filter.Tendsto (fun N => -f ↑N) Filter.atTop (nhds 0) → HasSum f a (SummationFilter.symmetricIco ℤ)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt

Cited by

3 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceContinuousAdd