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Theorems · Theorem · measure theory

MeasureTheory.Integrable.of_comp_fst

∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
  [MeasureTheory.SFinite μ] {f : α → E},
  MeasureTheory.Integrable (fun x => f x.1) (μ.prod ν) → ν ≠ 0 → MeasureTheory.Integrable f μ
Defined in
Mathlib.MeasureTheory.Integral.Prod
Cited by
1 results in Mathlib
Foundations
Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteMeasureTheory.SFinite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Integrable.comp_fst_iff · cited by 0Integrable.comp_fst_iffNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableMeasureTheory.SFinite · cited by 449MeasureTheory.SFiniteMeasureTheory.Measure.prod · cited by 353Measure.prodMeasureTheory.Integrable.swap · cited by 7Integrable.swapMeasureTheory.Integrable.of_comp_snd · cited by 2Integrable.of_comp_sndIntegrable.of_comp_fstCITED BYCITES

Cites8

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Cited by1

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