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Theorems · Theorem · measure theory

MeasureTheory.integrable_swap_iff

∀ {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 × β → E},
  MeasureTheory.Integrable (f ∘ Prod.swap) (ν.prod μ) ↔ MeasureTheory.Integrable f (μ.prod ν)
Defined in
Mathlib.MeasureTheory.Integral.Prod
Cited by
3 results in Mathlib
Foundations
Depth 224 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.swap · cited by 7Integrable.swapMeasureTheory.integrable_prod_iff' · cited by 4MeasureTheory.integrable_…MeasureTheory.intervalIntegral_intervalIntegral_swap · cited by 1MeasureTheory.intervalInt…NormedAddCommGroup · 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.prodMeasurableEquiv.measurableEmbedding · cited by 60MeasurableEquiv.measurabl…MeasureTheory.Measure.measurePreserving_swap · cited by 16Measure.measurePreserving…MeasureTheory.MeasurePreserving.integrable_comp_emb · cited by 9MeasurePreserving.integra…MeasurableEquiv.prodComm · cited by 8MeasurableEquiv.prodCommMeasureTheory.integrable_swap…CITED BYCITES

Cites10

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Cited by3

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