Theorems · Theorem · measure theory

MeasureTheory.setIntegral_norm_condExp_rpow_le

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {p : ℝ},
  1 ≤ p →
    ∀ {f : α → E} {s : Set α},
      MeasurableSet s →
        MeasureTheory.Integrable (fun x => ‖f x‖ ^ p) μ →
          ∫ (x : α) in s, ‖μ[f | m] x‖ ^ p ∂μ ≤ ∫ (x : α) in s, ‖f x‖ ^ p ∂μ

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Real

Cited by

1 results in Mathlib

Foundations

Depth 309 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace