Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.integral_add

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst_1 : NormedSpace ℝ E] {f g : MeasureTheory.SimpleFunc α E},
  MeasureTheory.Integrable (⇑f) μ →
    MeasureTheory.Integrable (⇑g) μ →
      MeasureTheory.SimpleFunc.integral μ (f + g) =
        MeasureTheory.SimpleFunc.integral μ f + MeasureTheory.SimpleFunc.integral μ g

Defined in

Mathlib.MeasureTheory.Integral.Bochner.L1

Cited by

1 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace