Theorems · Theorem · measure theory

Measurable.isLUB

∀ {α : Type u_1} {δ : Type u_4} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
  {mδ : MeasurableSpace δ} [inst_2 : LinearOrder α] [OrderTopology α] [SecondCountableTopology α] {ι : Sort u_5}
  [Countable ι] {f : ι → δ → α} {g : δ → α},
  (∀ (i : ι), Measurable (f i)) → (∀ (b : δ), IsLUB {a | ∃ i, f i b = a} (g b)) → Measurable g

If a function is the least upper bound of countably many measurable functions, then it is measurable.

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Order

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceLinearOrderOrderTopologySecondCountableTopologyCountable