Theorems · Theorem · measure theory

MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst

∀ {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} {s : Set α},
  (∀ (s : Set α), MeasurableSet s → μ s = 0 → T s = 0) →
    MeasureTheory.FinMeasAdditive μ T →
      ∀ (hs : MeasurableSet s) (hμs : μ s < ⊤) (x : E),
        MeasureTheory.L1.SimpleFunc.setToL1S T (MeasureTheory.Lp.simpleFunc.indicatorConst 1 hs ⋯ x) = (T s) x

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

2 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace