Theorems · Theorem · measure theory

MeasureTheory.lintegral_nnnorm_condExpL2_le

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {hm : m ≤ m0},
  MeasurableSet s →
    μ s ≠ ⊤ →
      ∀ (f : ↥(MeasureTheory.Lp ℝ 2 μ)),
        ∫⁻ (x : α) in s, ↑‖↑↑↑((MeasureTheory.condExpL2 ℝ ℝ hm) f) x‖₊ ∂μ ≤ ∫⁻ (x : α) in s, ↑‖↑↑f x‖₊ ∂μ

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

2 results in Mathlib

Foundations

Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound