Theorems · Theorem · functional analysis

LipschitzWith.norm_compLp_sub_le

∀ {α : Type u_1} {E : Type u_4} {F : Type u_5} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] {g : E → F} {c : NNReal} (hg : LipschitzWith c g)
  (g0 : g 0 = 0) (f f' : ↥(MeasureTheory.Lp E p μ)), ‖hg.compLp g0 f - hg.compLp g0 f'‖ ≤ ↑c * ‖f - f'‖

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup