Theorems · Theorem · measure theory

MeasureTheory.setToFun_congr_measure_of_integrable

∀ {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 C' : ℝ} {μ' : MeasureTheory.Measure α} (c' : ENNReal),
  c' ≠ ⊤ →
    μ' ≤ c' • μ →
      ∀ (hT : MeasureTheory.DominatedFinMeasAdditive μ T C) (hT' : MeasureTheory.DominatedFinMeasAdditive μ' T C')
        (f : α → E), MeasureTheory.Integrable f μ → MeasureTheory.setToFun μ T hT f = MeasureTheory.setToFun μ' T hT' f

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

5 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace