Theorems · Theorem · measure theory

MeasureTheory.setToFun_add

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {T : Set α → E →L[ℝ] F} {C : ℝ} {f g : α → E} (hT : MeasureTheory.DominatedFinMeasAdditive μ T C),
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g μ →
      MeasureTheory.setToFun μ T hT (f + g) = MeasureTheory.setToFun μ T hT f + MeasureTheory.setToFun μ T hT g

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

6 results in Mathlib

Foundations

Depth 242 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace