Theorems · Theorem · measure theory

MeasureTheory.condExpL1CLM_indicatorConstLp

∀ {α : Type u_1} {F' : Type u_3} [inst : NormedAddCommGroup F'] [inst_1 : NormedSpace ℝ F'] {m m0 : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {hm : m ≤ m0} [inst_2 : MeasureTheory.SigmaFinite (μ.trim hm)] {s : Set α}
  [inst_3 : CompleteSpace F'] (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x : F'),
  (MeasureTheory.condExpL1CLM F' hm μ) (MeasureTheory.indicatorConstLp 1 hs hμs x) =
    (MeasureTheory.condExpInd F' hm μ s) x

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

2 results in Mathlib

Foundations

Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFiniteCompleteSpace