Theorems · Theorem · commutative algebra

MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_weightedOrder_atTop_nhds_top

∀ {σ : Type u_3} {R : Type u_4} [inst : TopologicalSpace R] [inst_1 : CommSemiring R] {ι : Type u_5}
  {f : ι → MvPowerSeries σ R} [inst_2 : LinearOrder ι] [LocallyFiniteOrderBot ι] {w : σ → ℕ},
  Filter.Tendsto (fun i => MvPowerSeries.weightedOrder w (f i)) Filter.atTop (nhds ⊤) → Summable fun x => ∏ i ∈ x, f i

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

Defined in

Mathlib.RingTheory.MvPowerSeries.PiTopology

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceCommSemiringLinearOrderLocallyFiniteOrderBot