Theorems · Theorem · probability

MeasureTheory.AEStronglyMeasurable.comp_snd_map_prodMk

∀ {β : Type u_2} {mβ : MeasurableSpace β} {Ω : Type u_5} {F : Type u_6} {mΩ : MeasurableSpace Ω} (X : Ω → β)
  {μ : MeasureTheory.Measure Ω} [inst : TopologicalSpace F] {f : Ω → F},
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable (fun x => f x.2) (MeasureTheory.Measure.map (fun ω => (X ω, ω)) μ)

Defined in: Mathlib.Probability.Kernel.CondDistrib
Cited by: 3 results in Mathlib
Foundations: Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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Cites31

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

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Set.preimageproof · cited by 4,946
MeasurableSetproof · cited by 3,075
MeasureTheory.Measure.mapstatement and proof · cited by 858
AEMeasurableproof · cited by 840
MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
Set.univ_interproof · cited by 258

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.Integrable.comp_snd_map_prodMkproof · cited by 3
MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_idproof · cited by 2
ProbabilityTheory.aestronglyMeasurable_comp_snd_map_prodMk_iffproof · cited by 0