Theorems · Theorem · measure theory

MeasureTheory.UnifIntegrable.restrict

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup β] {f : ι → α → β} {p : ENNReal},
  MeasureTheory.UnifIntegrable f p μ → ∀ (E : Set α), MeasureTheory.UnifIntegrable f p (μ.restrict E)

Uniform integrability is preserved by restriction of the measure to a set.

Defined in

Mathlib.MeasureTheory.Function.UniformIntegrable

Cited by

0 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup