Theorems · Theorem · probability

ProbabilityTheory.Kernel.deterministic_map

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {f : α → β} (hf : Measurable f) {g : β → γ} (hg : Measurable g),
  (ProbabilityTheory.Kernel.deterministic f hf).map g = ProbabilityTheory.Kernel.deterministic (g ∘ f) ⋯

Defined in: Mathlib.Probability.Kernel.Composition.MapComap
Cited by: 2 results in Mathlib
Foundations: Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites9

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

MeasurableSpacestatement and proof · cited by 13,106
Measurablestatement and proof · cited by 1,499
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Measurable.compstatement and proof · cited by 234
ProbabilityTheory.Kernel.mapstatement and proof · cited by 84
ProbabilityTheory.Kernel.idproof · cited by 72
ProbabilityTheory.Kernel.deterministicstatement and proof · cited by 57
ProbabilityTheory.Kernel.map_comp_rightproof · cited by 10
ProbabilityTheory.Kernel.id_mapproof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.partialTraj_eq_prodproof · cited by 3
ProbabilityTheory.Kernel.partialTraj_succ_map_frestrictLe₂proof · cited by 1