Theorems · Theorem · sequences and series

SummationFilter.tsum_symmetricIcc_eq_tsum_symmetricIco

∀ {α : Type u_1} {f : ℤ → α} [inst : AddCommGroup α] [inst_1 : TopologicalSpace α] [ContinuousAdd α] [T2Space α],
  Summable f (SummationFilter.symmetricIcc ℤ) →
    Filter.Tendsto (fun N => -f ↑N) Filter.atTop (nhds 0) →
      ∑'[SummationFilter.symmetricIco ℤ] (b : ℤ), f b = ∑'[SummationFilter.symmetricIcc ℤ] (b : ℤ), f b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt

Cited by

1 results in Mathlib

Foundations

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

Assumes

AddCommGroupTopologicalSpaceContinuousAddT2Space