Theorems · Theorem · measure theory

MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left

∀ {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 T' : Set α → E →L[ℝ] F} {C C' : ℝ} (hT : MeasureTheory.DominatedFinMeasAdditive μ T C)
  (hT' : MeasureTheory.DominatedFinMeasAdditive μ T' C'),
  T = T' →
    ∀ (f : ↥(α →₁ₛ[μ] E)),
      (MeasureTheory.L1.SimpleFunc.setToL1SCLM α E μ hT) f = (MeasureTheory.L1.SimpleFunc.setToL1SCLM α E μ hT') f

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

1 results in Mathlib

Foundations

Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace