Theorems · Theorem · commutative algebra

PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top

∀ (R : Type u_1) [inst : TopologicalSpace R] [inst_1 : CommSemiring R] {ι : Type u_2} [inst_2 : LinearOrder ι]
  [LocallyFiniteOrderBot ι] {f : ι → PowerSeries R},
  Filter.Tendsto (fun i => (f i).order) Filter.atTop (nhds ⊤) → Summable fun x => ∏ i ∈ x, f i

If the order of a family of PowerSeries tends to infinity, the collection of all possible products over Finset is summable.

Defined in

Mathlib.RingTheory.PowerSeries.PiTopology

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommSemiringLinearOrderLocallyFiniteOrderBot