Theorems · Theorem · measure theory

MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α} {hm : m ≤ m0}
  (hs : MeasurableSet s) (hμs : μ s ≠ ⊤),
  MeasurableSet t →
    μ t ≠ ⊤ →
      ∫⁻ (a : α) in t, ↑‖↑↑↑((MeasureTheory.condExpL2 ℝ ℝ hm) (MeasureTheory.indicatorConstLp 2 hs hμs 1)) a‖₊ ∂μ ≤
        μ (s ∩ t)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

2 results in Mathlib

Foundations

Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound