Theorems · Theorem · probability
ProbabilityTheory.Kernel.traj_map_frestrictLe_of_le
∀ {X : ℕ → Type u_1} [inst : (n : ℕ) → MeasurableSpace (X n)]
{κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))}
[inst_1 : ∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] {a b : ℕ} (hab : a ≤ b),
(ProbabilityTheory.Kernel.traj κ b).map (Preorder.frestrictLe a) =
ProbabilityTheory.Kernel.deterministic (Preorder.frestrictLe₂ hab) ⋯- Cited by
- 0 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- Finset.Iicstatement and proof · cited by 280
- ProbabilityTheory.IsMarkovKernelstatement and proof · cited by 124
- ProbabilityTheory.Kernel.mapstatement · cited by 84
- ProbabilityTheory.Kernel.deterministicstatement and proof · cited by 57
- Preorder.frestrictLestatement · cited by 43
- ProbabilityTheory.Kernel.trajstatement · cited by 26
- Preorder.frestrictLe₂statement and proof · cited by 23
- Preorder.measurable_frestrictLe₂statement and proof · cited by 12
- ProbabilityTheory.Kernel.traj_map_frestrictLeproof · cited by 10
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