Theorems · Theorem · measure theory

FDerivMeasurableAux.norm_sub_le_of_mem_A

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {c : 𝕜},
  1 < ‖c‖ →
    ∀ {r ε : ℝ},
      0 < ε →
        0 < r →
          ∀ {x : E} {L₁ L₂ : E →L[𝕜] F},
            x ∈ FDerivMeasurableAux.A f L₁ r ε → x ∈ FDerivMeasurableAux.A f L₂ r ε → ‖L₁ - L₂‖ ≤ 4 * ‖c‖ * ε

Defined in

Mathlib.Analysis.Calculus.FDeriv.Measurable

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace