Theorems · Theorem · measure theory

Integrable.norm_condExp_rpow_le

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {α : Type u_2} {f : α → E}
  {m mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p : ℝ},
  1 ≤ p → MeasureTheory.Integrable (fun x => ‖f x‖ ^ p) μ → (fun x => ‖μ[f | m] x‖ ^ p) ≤ᵐ[μ] μ[fun x => ‖f x‖ ^ p | m]

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondJensen

Cited by

3 results in Mathlib

Foundations

Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace