Theorems · Theorem · measure theory

MeasureTheory.measurable_uncurry_of_continuous_of_measurable

∀ {α : Type u_5} {β : Type u_6} {ι : Type u_7} [inst : TopologicalSpace ι] [TopologicalSpace.MetrizableSpace ι]
  [inst_2 : MeasurableSpace ι] [SecondCountableTopology ι] [OpensMeasurableSpace ι] {mβ : MeasurableSpace β}
  [inst_5 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β] [BorelSpace β] {m : MeasurableSpace α}
  {u : ι → α → β},
  (∀ (x : α), Continuous fun i => u i x) → (∀ (i : ι), Measurable (u i)) → Measurable (Function.uncurry u)

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.MetrizableSpaceMeasurableSpaceSecondCountableTopologyOpensMeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceBorelSpace