Theorems · Theorem · measure theory

MeasureTheory.condExpIndL1Fin_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)]
  (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ⊤) (hμt : μ t ≠ ⊤),
  Disjoint s t →
    ∀ (x : G),
      MeasureTheory.condExpIndL1Fin hm ⋯ ⋯ x =
        MeasureTheory.condExpIndL1Fin hm hs hμs x + MeasureTheory.condExpIndL1Fin hm ht hμt x

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

1 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite