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Theorems · Theorem · measure theory

MeasureTheory.Measure.measurePreserving_swap

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ],
  MeasureTheory.MeasurePreserving Prod.swap (μ.prod ν) (ν.prod μ)
Defined in
Mathlib.MeasureTheory.Measure.Prod
Cited by
16 results in Mathlib
Foundations
Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite

Around this declaration

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

MeasureTheory.integral_prod_swap · cited by 3MeasureTheory.integral_pr…MeasureTheory.integrable_swap_iff · cited by 3MeasureTheory.integrable_…MeasureTheory.NullMeasurableSet.left_of_prod · cited by 2NullMeasurableSet.left_of…MeasureTheory.measurePreserving_prod_add_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_add_swap_right · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_div_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_inv_mul_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_mul_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_mul_swap_right · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_prod_neg_add_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.lintegral_prod_swap · cited by 2MeasureTheory.lintegral_p…MeasureTheory.measurePreserving_prod_sub_swap · cited by 2MeasureTheory.measurePres…MeasureTheory.measurePreserving_sub_prod · cited by 1MeasureTheory.measurePres…MeasureTheory.measurePreserving_add_prod · cited by 0MeasureTheory.measurePres…MeasureTheory.measurePreserving_div_prod · cited by 0MeasureTheory.measurePres…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.SFinite · cited by 449MeasureTheory.SFiniteMeasureTheory.Measure.prod · cited by 353Measure.prodMeasureTheory.MeasurePreserving · cited by 259MeasureTheory.MeasurePres…measurable_swap · cited by 42measurable_swapMeasureTheory.Measure.prod_swap · cited by 14Measure.prod_swapMeasure.measurePreserving_swapCITED BYCITES

Cites7

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

Cited by16

Results whose statement or proof uses this declaration.