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Theorems · Theorem · measure theory

MeasureTheory.Measure.map_snd_prod

∀ {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.Measure.map Prod.snd (μ.prod ν) = μ Set.univ • ν
Defined in
Mathlib.MeasureTheory.Measure.Prod
Cited by
11 results in Mathlib
Foundations
Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpaceMeasureTheory.SFinite

Around this declaration

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

MeasureTheory.measurePreserving_snd · cited by 4MeasureTheory.measurePres…MeasureTheory.MemLp.comp_snd · cited by 4MemLp.comp_sndMeasureTheory.prod_withDensity₀ · cited by 3MeasureTheory.prod_withDe…ProbabilityTheory.indepFun_prod · cited by 3ProbabilityTheory.indepFu…MeasureTheory.prod_withDensity_right₀ · cited by 2MeasureTheory.prod_withDe…MeasureTheory.partialTraj_const_restrict₂ · cited by 1MeasureTheory.partialTraj…LinearMap.exists_map_addHaar_eq_smul_addHaar' · cited by 1LinearMap.exists_map_addH…ProbabilityTheory.Kernel.snd_prod · cited by 1Kernel.snd_prodMeasureTheory.FiniteMeasure.map_snd_prod · cited by 0FiniteMeasure.map_snd_prodMeasureTheory.ProbabilityMeasure.map_snd_prod · cited by 0ProbabilityMeasure.map_sn…ProbabilityTheory.condDistrib_snd_prod · cited by 0ProbabilityTheory.condDis…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.univ · cited by 3945Set.univMeasurableSet · cited by 3075MeasurableSetMeasureTheory.Measure.map · cited by 858Measure.mapMeasureTheory.SFinite · cited by 449MeasureTheory.SFiniteMeasureTheory.Measure.prod · cited by 353Measure.prodMeasureTheory.Measure.ext · cited by 308Measure.extMeasureTheory.Measure.map_apply · cited by 139Measure.map_applymeasurable_snd · cited by 94measurable_sndMeasureTheory.Measure.prod_prod · cited by 38Measure.prod_prodMeasure.map_snd_prodCITED BYCITES

Cites14

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

Cited by11

Results whose statement or proof uses this declaration.