Theorems · Definition · measure theory

MeasureTheory.condExpL1CLM

{α : Type u_1} →
  (F' : Type u_3) →
    [inst : NormedAddCommGroup F'] →
      [inst_1 : NormedSpace ℝ F'] →
        {m m0 : MeasurableSpace α} →
          (hm : m ≤ m0) →
            (μ : MeasureTheory.Measure α) →
              [CompleteSpace ↥(MeasureTheory.Lp F' 1 μ)] →
                [MeasureTheory.SigmaFinite (μ.trim hm)] → ↥(MeasureTheory.Lp F' 1 μ) →L[ℝ] ↥(MeasureTheory.Lp F' 1 μ)

Conditional expectation of a function as a linear map from α →₁[μ] F' to itself.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

11 results in Mathlib

Foundations

Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite