Theorems · Theorem · measure theory

MeasurableEmbedding.integrableOn_range_iff_comap

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] [inst_2 : MeasurableSpace β] {e : α → β},
  MeasurableEmbedding e →
    ∀ {f : β → ε} {μ : MeasureTheory.Measure β},
      MeasureTheory.IntegrableOn f (Set.range e) μ ↔ MeasureTheory.Integrable (f ∘ e) (MeasureTheory.Measure.comap e μ)

Defined in: Mathlib.MeasureTheory.Integral.IntegrableOn
Cited by: 1 results in Mathlib
Foundations: Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace ContinuousENorm MeasurableSpace

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.rangestatement · cited by 4,705
MeasureTheory.Integrablestatement and proof · cited by 1,367
MeasureTheory.IntegrableOnstatement and proof · cited by 548
ContinuousENormstatement and proof · cited by 290
Set.Subset.rflproof · cited by 255
MeasurableEmbeddingstatement and proof · cited by 170
MeasureTheory.Measure.comapstatement and proof · cited by 96
Set.preimage_rangeproof · cited by 38

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.integrableOn_iff_comap_subtypeValproof · cited by 1