Theorems · Theorem · measure theory

MeasureTheory.UnifIntegrable.add

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup β] {f g : ι → α → β} {p : ENNReal},
  MeasureTheory.UnifIntegrable f p μ →
    MeasureTheory.UnifIntegrable g p μ →
      1 ≤ p →
        (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ) →
          (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (g i) μ) → MeasureTheory.UnifIntegrable (f + g) p μ

Defined in

Mathlib.MeasureTheory.Function.UniformIntegrable

Cited by

2 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup