Theorems · Theorem · measure theory

MeasureTheory.locallyIntegrable_comap

∀ {X : Type u_1} {ε : Type u_3} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace ε]
  [inst_3 : ContinuousENorm ε] {f : X → ε} {μ : MeasureTheory.Measure X} {s : Set X},
  MeasurableSet s →
    (MeasureTheory.LocallyIntegrable (fun x => f ↑x) (MeasureTheory.Measure.comap Subtype.val μ) ↔
      MeasureTheory.LocallyIntegrableOn f s μ)

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

1 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpaceContinuousENorm