Theorems · Theorem · sequences and series

Multipliable.hasProd_iff_tendsto_nat

∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] {m : M} [T2Space M] {f : ℕ → M},
  Multipliable f → (HasProd f m ↔ Filter.Tendsto (fun n => ∏ i ∈ Finset.range n, f i) Filter.atTop (nhds m))

Defined in

Mathlib.Topology.Algebra.InfiniteSum.NatInt

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceT2Space