Theorems · Theorem · measure theory

MeasureTheory.condExpIndL1Fin_add

∀ {α : Type u_1} {G : Type u_4} [inst : NormedAddCommGroup G] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s : Set α} [inst_1 : NormedSpace ℝ G] {hm : m ≤ m0} [inst_2 : MeasureTheory.SigmaFinite (μ.trim hm)]
  (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x y : G),
  MeasureTheory.condExpIndL1Fin hm hs hμs (x + y) =
    MeasureTheory.condExpIndL1Fin hm hs hμs x + MeasureTheory.condExpIndL1Fin hm hs hμs y

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

1 results in Mathlib

Foundations

Depth 277 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite