Theorems · Theorem · measure theory

AEMeasurable.biSup

∀ {α : Type u_1} {δ : Type u_4} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
  {mδ : MeasurableSpace δ} [inst_2 : ConditionallyCompleteLinearOrder α] [OrderTopology α] [SecondCountableTopology α]
  {ι : Type u_5} {μ : MeasureTheory.Measure δ} (s : Set ι) {f : ι → δ → α},
  s.Countable → (∀ i ∈ s, AEMeasurable (f i) μ) → AEMeasurable (fun b => ⨆ i ∈ s, f i b) μ

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Order

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceConditionallyCompleteLinearOrderOrderTopologySecondCountableTopology