Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_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) {t : Set α},
  MeasurableSet t → μ t ≠ ⊤ → ∫⁻ (a : α) in t, ↑‖↑↑(MeasureTheory.condExpIndSMul hm hs hμs x) a‖₊ ∂μ ≤ μ (s ∩ t) * ↑‖x‖₊

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

2 results in Mathlib

Foundations

Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace