English
The infinite product measure over a sequence X i is well-defined via a traj-construction combined with the pi-product, yielding a probability measure on the product space.
Русский
Бесконечная произведения мер по последовательности X_i есть определима через траекторию (traj) и произведение по π, образующая нормированную меру на произведение пространств.
LaTeX
$$$\text{infinitePiNat } :\text{Measure } ((n:\N)\to X n)$ defined as $(traj (fun n \mapsto const _ (\mu (n+1))) 0) \circₘ (Measure.pi (fun i : Iic 0 \mapsto μ i))$$$
Lean4
/-- Infinite product measure indexed by `ℕ`. This is an auxiliary construction, you should use
the generic product measure `Measure.infinitePi`. -/
noncomputable def infinitePiNat : Measure (Π n, X n) :=
(traj (fun n ↦ const _ (μ (n + 1))) 0) ∘ₘ (Measure.pi (fun i : Iic 0 ↦ μ i))
