Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.integral_add_measure

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

Defined in

Mathlib.MeasureTheory.Integral.Bochner.L1

Cited by

0 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace