Theorems · Theorem · measure theory

MeasureTheory.Integrable.ae_eq_of_forall_setIntegral_eq

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] (f g : α → E),
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g μ →
      (∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫ (x : α) in s, f x ∂μ = ∫ (x : α) in s, g x ∂μ) → f =ᵐ[μ] g

Defined in

Mathlib.MeasureTheory.Function.AEEqOfIntegral

Cited by

3 results in Mathlib

Foundations

Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace