Theorems · Theorem · measure theory

MeasureTheory.condExpL1_eq

∀ {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)] {f : α → F'}
  [inst_3 : CompleteSpace F'] (hf : MeasureTheory.Integrable f μ),
  MeasureTheory.condExpL1 hm μ f = (MeasureTheory.condExpL1CLM F' hm μ) (MeasureTheory.Integrable.toL1 f hf)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

4 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFiniteCompleteSpace