Theorems · Inductive type · several complex variables

HasFPowerSeriesWithinOnBall

{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] → (E → F) → FormalMultilinearSeries 𝕜 E F → Set E → E → ENNReal → Prop

Analogue of HasFPowerSeriesOnBall where convergence is required only on a set s. We also require convergence at x as the behavior of this notion is very bad otherwise.

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

83 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace