Theorems · Theorem · measure theory

MeasureTheory.setToFun_eq

∀ {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 : α → E} [hF : CompleteSpace F] (hT : MeasureTheory.DominatedFinMeasAdditive μ T C)
  (hf : MeasureTheory.Integrable f μ),
  MeasureTheory.setToFun μ T hT f = (MeasureTheory.L1.setToL1 hT) (MeasureTheory.Integrable.toL1 f hf)

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

20 results in Mathlib

Foundations

Depth 241 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace