Documentation

BrownianMotion.Gaussian.StochasticProcesses

theorem modification_of_indistinduishable {T : Type u_1} {Ω : Type u_2} {E : Type u_3} { : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {X Y : TΩE} (h : ∀ᵐ (ω : Ω) P, ∀ (t : T), X t ω = Y t ω) (t : T) :
X t =ᵐ[P] Y t
theorem indistinduishable_of_modification {T : Type u_1} {Ω : Type u_2} {E : Type u_3} { : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {X Y : TΩE} [TopologicalSpace E] [TopologicalSpace T] [TopologicalSpace.SeparableSpace T] [T2Space E] (hX : ∀ᵐ (ω : Ω) P, Continuous fun (t : T) => X t ω) (hY : ∀ᵐ (ω : Ω) P, Continuous fun (t : T) => Y t ω) (h : ∀ (t : T), X t =ᵐ[P] Y t) :
∀ᵐ (ω : Ω) P, ∀ (t : T), X t ω = Y t ω