Theorems · Theorem · sequences and series

HasProd.hasProd_symmetricIco_of_hasProd_symmetricIcc

∀ {α : Type u_1} {f : ℤ → α} [inst : CommGroup α] [inst_1 : TopologicalSpace α] [ContinuousMul α] {a : α},
  HasProd f a (SummationFilter.symmetricIcc ℤ) →
    Filter.Tendsto (fun N => (f ↑N)⁻¹) Filter.atTop (nhds 1) → HasProd f a (SummationFilter.symmetricIco ℤ)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.ConditionalInt

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommGroupTopologicalSpaceContinuousMul