Theorems · Theorem · measure theory

MeasureTheory.condExpL1CLM_smul

∀ {α : Type u_1} {F' : Type u_3} {𝕜 : Type u_6} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup F']
  [inst_2 : NormedSpace 𝕜 F'] [inst_3 : NormedSpace ℝ F'] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {hm : m ≤ m0} [inst_4 : MeasureTheory.SigmaFinite (μ.trim hm)] [inst_5 : CompleteSpace F'] (c : 𝕜)
  (f : ↥(MeasureTheory.Lp F' 1 μ)),
  (MeasureTheory.condExpL1CLM F' hm μ) (c • f) = c • (MeasureTheory.condExpL1CLM F' hm μ) f

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

0 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedSpaceMeasureTheory.SigmaFiniteCompleteSpace