Theorems · Theorem · measure theory

MeasureTheory.LipschitzWith.integrable_comp_iff_of_antilipschitz

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup β] [inst_1 : NormedAddCommGroup γ] {K K' : NNReal} {f : α → β} {g : β → γ},
  LipschitzWith K g →
    AntilipschitzWith K' g → g 0 = 0 → (MeasureTheory.Integrable (g ∘ f) μ ↔ MeasureTheory.Integrable f μ)

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroup