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Theorems · Theorem · measure theory

Measurable.prodMap

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {m : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} [inst : MeasurableSpace δ] {f : α → β} {g : γ → δ},
  Measurable f → Measurable g → Measurable (Prod.map f g)
Defined in
Mathlib.MeasureTheory.MeasurableSpace.Constructions
Cited by
19 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace

Around this declaration

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

MeasureTheory.Measure.map_prod_map · cited by 7Measure.map_prod_mapMeasureTheory.Measure.compProd_map · cited by 4Measure.compProd_mapProbabilityTheory.Kernel.map_prod_map · cited by 4Kernel.map_prod_mapProbabilityTheory.eq_condKernel_of_measure_eq_compProd · cited by 3ProbabilityTheory.eq_cond…MeasureTheory.Measure.map_conv_addMonoidHom · cited by 3Measure.map_conv_addMonoi…ProbabilityTheory.Kernel.partialTraj_eq_prod · cited by 3Kernel.partialTraj_eq_prodProbabilityTheory.HasCondDistrib.comp_left · cited by 2HasCondDistrib.comp_leftMeasureTheory.partialTraj_const_restrict₂ · cited by 1MeasureTheory.partialTraj…ProbabilityTheory.HasCondDistrib.comp_right · cited by 1HasCondDistrib.comp_rightProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_comp_trim · cited by 1ProbabilityTheory.condInd…ProbabilityTheory.Kernel.compProd_fst_borelMarkovFromReal_eq_comapRight_compProd · cited by 1Kernel.compProd_fst_borel…ProbabilityTheory.Kernel.traj_eq_prod · cited by 1Kernel.traj_eq_prodProbabilityTheory.Kernel.partialTraj_compProd_eq_map_traj · cited by 1Kernel.partialTraj_compPr…ProbabilityTheory.Kernel.deterministic_parallelComp_deterministic · cited by 1Kernel.deterministic_para…MeasureTheory.ProbabilityMeasure.map_prod_map · cited by 0ProbabilityMeasure.map_pr…MeasurableSpace · cited by 13106MeasurableSpaceMeasurable · cited by 1499MeasurableMeasurable.comp · cited by 234Measurable.compMeasurable.prodMk · cited by 115Measurable.prodMkmeasurable_snd · cited by 94measurable_sndmeasurable_fst · cited by 79measurable_fstMeasurable.prodMapCITED BYCITES

Cites6

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Cited by19

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