Theorems · Theorem · measure theory

MeasureTheory.setToFun_add_measure

∀ {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 T' : Set α → E →L[ℝ] F} {C C' : ℝ} {f : α → E} {ν : MeasureTheory.Measure α}
  (hTμ : MeasureTheory.DominatedFinMeasAdditive μ T C) (hTν : MeasureTheory.DominatedFinMeasAdditive ν T' C'),
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable f ν →
      MeasureTheory.setToFun (μ + ν) (T + T') ⋯ f = MeasureTheory.setToFun μ T hTμ f + MeasureTheory.setToFun ν T' hTν f

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

2 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace