Theorems · Theorem · several complex variables

HasFPowerSeriesOnBall.mono

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {p : FormalMultilinearSeries 𝕜 E F} {x : E} {r r' : ENNReal},
  HasFPowerSeriesOnBall f p x r → 0 < r' → r' ≤ r → HasFPowerSeriesOnBall f p x r'

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

10 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace