Theorems · Definition · measure theory

MeasureTheory.condExpIndL1Fin

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

Conditional expectation of the indicator of a measurable set with finite measure, as a function in L1.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

12 results in Mathlib

Foundations

Depth 276 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite