Theorems · Theorem · measure theory

MeasurableEmbedding.integrableAtFilter_map_iff

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {l : Filter α} [inst_2 : MeasurableSpace β] {e : α → β},
  MeasurableEmbedding e →
    ∀ {f : β → ε},
      MeasureTheory.IntegrableAtFilter f (Filter.map e l) (MeasureTheory.Measure.map e μ) ↔
        MeasureTheory.IntegrableAtFilter (f ∘ e) l μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormMeasurableSpace