Theorems · Theorem · measure theory

MeasureTheory.setIntegral_abs_condExp_le

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] [inst_3 : Lattice E] [HasSolidNorm E] [IsOrderedAddMonoid E]
  [IsOrderedModule ℝ E] {s : Set α},
  MeasurableSet s → ∀ (f : α → E), ∫ (x : α) in s, |μ[f | m] x| ∂μ ≤ ∫ (x : α) in s, |f x| ∂μ

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Real

Cited by

1 results in Mathlib

Foundations

Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceLatticeHasSolidNormIsOrderedAddMonoidIsOrderedModule