Theorems · Theorem · several complex variables

FormalMultilinearSeries.radius_prod_eq_min

∀ {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] (p : FormalMultilinearSeries 𝕜 E F)
  (q : FormalMultilinearSeries 𝕜 E G), (p.prod q).radius = min p.radius q.radius

The radius of the Cartesian product of two formal series is the minimum of their radii.

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace