Theorems · Theorem · measure theory

MeasureTheory.condExpIndL1_disjoint_union

∀ {α : Type u_1} {G : Type u_4} [inst : NormedAddCommGroup G] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s t : Set α} [inst_1 : NormedSpace ℝ G] {hm : m ≤ m0} [inst_2 : MeasureTheory.SigmaFinite (μ.trim hm)],
  MeasurableSet s →
    MeasurableSet t →
      μ s ≠ ⊤ →
        μ t ≠ ⊤ →
          Disjoint s t →
            ∀ (x : G),
              MeasureTheory.condExpIndL1 hm μ (s ∪ t) x =
                MeasureTheory.condExpIndL1 hm μ s x + MeasureTheory.condExpIndL1 hm μ t x

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

1 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite