Theorems · Theorem · probability

ProbabilityTheory.Kernel.partialTraj_self

∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)}
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))} (a : ℕ),
  ProbabilityTheory.Kernel.partialTraj κ a a = ProbabilityTheory.Kernel.id

Defined in: Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj
Cited by: 5 results in Mathlib
Foundations: Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites11

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

Finsetstatement · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
le_rflproof · cited by 1,558
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Finset.Iicstatement and proof · cited by 280
ProbabilityTheory.Kernel.idstatement and proof · cited by 72
ProbabilityTheory.Kernel.deterministicproof · cited by 57
ProbabilityTheory.Kernel.partialTrajstatement · cited by 44
Preorder.frestrictLe₂proof · cited by 23
Preorder.measurable_frestrictLe₂proof · cited by 12
ProbabilityTheory.Kernel.partialTraj_leproof · cited by 8

Cited by5

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.partialTraj_succ_selfproof · cited by 6
ProbabilityTheory.Kernel.partialTraj_succ_of_leproof · cited by 3
ProbabilityTheory.Kernel.partialTraj_comp_partialTrajproof · cited by 3
ProbabilityTheory.Kernel.partialTraj_eq_prodproof · cited by 3
ProbabilityTheory.Kernel.partialTraj_le_defproof · cited by 1