Theorems · Theorem · measure theory

MeasureTheory.integral_union_eq_left_of_ae_aux

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {f : X → E} {s t : Set X} {μ : MeasureTheory.Measure X},
  (∀ᵐ (x : X) ∂μ.restrict t, f x = 0) →
    MeasureTheory.StronglyMeasurable f →
      MeasureTheory.IntegrableOn f (s ∪ t) μ → ∫ (x : X) in s ∪ t, f x ∂μ = ∫ (x : X) in s, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

1 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace