Theorems · Theorem · functional analysis

LipschitzWith.coeFn_compLp

∀ {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 : ↥(MeasureTheory.Lp E p μ)), ↑↑(hg.compLp g0 f) =ᵐ[μ] g ∘ ↑↑f

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

3 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup