Theorems · Theorem · measure theory

MeasureTheory.integrable_add_of_disjoint

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] {μ : MeasureTheory.Measure α}
  {f g : α → E},
  Disjoint (Function.support f) (Function.support g) →
    MeasureTheory.StronglyMeasurable f →
      MeasureTheory.StronglyMeasurable g →
        (MeasureTheory.Integrable (f + g) μ ↔ MeasureTheory.Integrable f μ ∧ MeasureTheory.Integrable g μ)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

0 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup