Theorems · Theorem · measure theory

MeasureTheory.ae_bdd_norm_condExp_of_ae_bdd_norm

∀ {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] {R : ℝ} {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

2 results in Mathlib

Foundations

Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace