Theorems · Theorem · measure theory

MeasureTheory.locallyIntegrable_map_homeomorph

∀ {X : Type u_1} {Y : Type u_2} {ε'' : Type u_5} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X]
  [inst_2 : MeasurableSpace Y] [inst_3 : TopologicalSpace Y] [inst_4 : TopologicalSpace ε'']
  [inst_5 : ESeminormedAddMonoid ε''] [BorelSpace X] [BorelSpace Y] (e : X ≃ₜ Y) {f : Y → ε''}
  {μ : MeasureTheory.Measure X},
  MeasureTheory.LocallyIntegrable f (MeasureTheory.Measure.map (⇑e) μ) ↔ MeasureTheory.LocallyIntegrable (f ∘ ⇑e) μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceMeasurableSpaceTopologicalSpaceTopologicalSpaceESeminormedAddMonoidBorelSpaceBorelSpace