Theorems · Theorem · measure theory

MeasureTheory.setToFun_congr_measure_of_add_right

∀ {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 C' : ℝ} {μ' : MeasureTheory.Measure α}
  (hT_add : MeasureTheory.DominatedFinMeasAdditive (μ + μ') T C') (hT : MeasureTheory.DominatedFinMeasAdditive μ T C)
  (f : α → E),
  MeasureTheory.Integrable f (μ + μ') → MeasureTheory.setToFun (μ + μ') T hT_add f = MeasureTheory.setToFun μ T hT f

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

2 results in Mathlib

Foundations

Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace