Theorems · Theorem · measure theory

MeasureTheory.L1.setToL1_const

∀ {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}
  [inst_4 : CompleteSpace F] {T : Set α → E →L[ℝ] F} {C : ℝ} [inst_5 : MeasureTheory.IsFiniteMeasure μ]
  (hT : MeasureTheory.DominatedFinMeasAdditive μ T C) (x : E),
  (MeasureTheory.L1.setToL1 hT) (MeasureTheory.indicatorConstLp 1 ⋯ ⋯ x) = (T Set.univ) x

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

0 results in Mathlib

Foundations

Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.IsFiniteMeasure