Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.setIntegral_inter_add_sdiff

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedAddCommGroup G] {μ : MeasureTheory.VectorMeasure X F} {f : X → E}
  {s t : Set X} [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace ℝ G]
  {B : E →L[ℝ] F →L[ℝ] G},
  MeasurableSet s →
    MeasurableSet t →
      μ.IntegrableOn f s →
        ∫ᵛ (x : X) in s ∩ t, f x ∂[B; μ] + ∫ᵛ (x : X) in s \ t, f x ∂[B; μ] = ∫ᵛ (x : X) in s, f x ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

0 results in Mathlib

Foundations

Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace