Theorems · Theorem · measure theory

MeasureTheory.condExpInd_nonneg

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {hm : m ≤ m0}
  [inst : MeasureTheory.SigmaFinite (μ.trim hm)] {E : Type u_7} [inst_1 : NormedAddCommGroup E]
  [inst_2 : PartialOrder E] [inst_3 : NormedSpace ℝ E] [IsOrderedModule ℝ E],
  MeasurableSet s → μ s ≠ ⊤ → ∀ (x : E), 0 ≤ x → 0 ≤ (MeasureTheory.condExpInd E hm μ s) x

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

1 results in Mathlib

Foundations

Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteNormedAddCommGroupPartialOrderNormedSpaceIsOrderedModule