Theorems · Theorem · measure theory

MeasureTheory.lintegral_nnnorm_condExpIndSMul_le

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s : Set α} [inst_1 : NormedSpace ℝ G] (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x : G)
  [MeasureTheory.SigmaFinite (μ.trim hm)],
  ∫⁻ (a : α), ↑‖↑↑(MeasureTheory.condExpIndSMul hm hs hμs x) a‖₊ ∂μ ≤ μ s * ↑‖x‖₊

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

1 results in Mathlib

Foundations

Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite