Theorems · Theorem · measure theory

MeasureTheory.ae_bdd_abs_condExp_of_ae_bdd_abs

∀ {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] {R : E} {f : α → E}, (∀ᵐ (x : α) ∂μ, |f x| ≤ R) → ∀ᵐ (x : α) ∂μ, |μ[f | m] x| ≤ R

If |f| is bounded almost everywhere by R, then so is its conditional expectation.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Real

Cited by

0 results in Mathlib

Foundations

Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceLatticeHasSolidNormIsOrderedAddMonoidIsOrderedModule