Theorems · Theorem · measure theory

Measurable.sSup

∀ {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} {f : ι → δ → α} {s : Set ι},
  s.Countable → (∀ i ∈ s, Measurable (f i)) → Measurable fun x => sSup ((fun i => f i x) '' s)

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Order

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceConditionallyCompleteLinearOrderOrderTopologySecondCountableTopology