Theorems · Theorem · several complex variables

HasFPowerSeriesWithinOnBall.prod

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} {G : Type u_5}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {e : E} {f : E → F} {g : E → G} {r s : ENNReal} {t : Set E}
  {p : FormalMultilinearSeries 𝕜 E F} {q : FormalMultilinearSeries 𝕜 E G},
  HasFPowerSeriesWithinOnBall f p t e r →
    HasFPowerSeriesWithinOnBall g q t e s → HasFPowerSeriesWithinOnBall (fun x => (f x, g x)) (p.prod q) t e (min r s)

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace