Theorems · Definition · measure theory

MeasureTheory.condExpInd

{α : Type u_1} →
  (G : Type u_4) →
    [inst : NormedAddCommGroup G] →
      [inst_1 : NormedSpace ℝ G] →
        {m m0 : MeasurableSpace α} →
          (hm : m ≤ m0) →
            (μ : MeasureTheory.Measure α) →
              [MeasureTheory.SigmaFinite (μ.trim hm)] → Set α → G →L[ℝ] ↥(MeasureTheory.Lp G 1 μ)

Conditional expectation of the indicator of a set, as a linear map from G to L1.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

18 results in Mathlib

Foundations

Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite