Theorems · Theorem · probability

ProbabilityTheory.Locally.localSeq.congr_simp

∀ {ι : Type u_1} {Ω : Type u_2} {E : Type u_3} {mΩ : MeasurableSpace Ω} {P P_1 : MeasureTheory.Measure Ω}
  (e_P : P = P_1) [inst : LinearOrder ι] {𝓕 𝓕_1 : MeasureTheory.Filtration ι mΩ} (e_𝓕 : 𝓕 = 𝓕_1) {X X_1 : ι → Ω → E}
  (e_X : X = X_1) {p p_1 : (ι → Ω → E) → Prop} (e_p : p = p_1) [inst_1 : OrderBot ι] [inst_2 : TopologicalSpace ι]
  [inst_3 : OrderTopology ι] [inst_4 : Zero E] (hX : ProbabilityTheory.Locally p 𝓕 X P) (a a_1 : ℕ),
  a = a_1 → ∀ (a_2 a_3 : Ω), a_2 = a_3 → hX.localSeq a a_2 = ⋯.localSeq a_1 a_3

Defined in

Mathlib.Probability.Process.LocalProperty

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderOrderBotTopologicalSpaceOrderTopologyZero