Theorems · Theorem · measure theory

MeasureTheory.L1.setToFun_eq_setToL1

∀ {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} [inst_4 : CompleteSpace F] (hT : MeasureTheory.DominatedFinMeasAdditive μ T C)
  (f : ↥(MeasureTheory.Lp E 1 μ)), MeasureTheory.setToFun μ T hT ↑↑f = (MeasureTheory.L1.setToL1 hT) f

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

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace