Theorems · Theorem · measure theory

MeasureTheory.condExpIndSMul_nonneg

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {hm : m ≤ m0} {E : Type u_10}
  [inst : NormedAddCommGroup E] [inst_1 : PartialOrder E] [inst_2 : NormedSpace ℝ E] [IsOrderedModule ℝ E]
  [MeasureTheory.SigmaFinite (μ.trim hm)] (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x : E),
  0 ≤ x → 0 ≤ᵐ[μ] ↑↑(MeasureTheory.condExpIndSMul hm hs hμs x)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

1 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupPartialOrderNormedSpaceIsOrderedModuleMeasureTheory.SigmaFinite