Manuscript En05-B@1 · En05-B.tex · section · 8b626460

Euclidean convergence of both past constructions

Euclidean convergence of both past constructions · lines 834–855

Events are embedded by

(x, s) ⟼ (s h_{n}, z_{n} (x)) .

For embedded terminal event $q = (T h_{n}, z_{n} (A))$ , define

J_{n, met}^{-} (q) J_{n, sch}^{-} (q) = {(s h_{n}, z_{n} (x)) : s \leq T, d_{n} (x, A) \leq T - s}, = {(s h_{n}, z_{n} (x)) : s \leq T, a scheduled path joins (x, s) to (A, T)} .

The continuum past is

J_{c}^{-} (q) = {(t, x) : t \leq t_{q}, ∥ x - x_{q} ∥_{2} \leq c (t_{q} - t)} .

Displayed formulas in this passage

unlabeled · line 837
$(x, s) ⟼ (s h_{n}, z_{n} (x)) .$
unlabeled · line 841
$J_{n, met}^{-} (q) J_{n, sch}^{-} (q) = {(s h_{n}, z_{n} (x)) : s \leq T, d_{n} (x, A) \leq T - s}, = {(s h_{n}, z_{n} (x)) : s \leq T, a scheduled path joins (x, s) to (A, T)} .$
unlabeled · line 851
$J_{c}^{-} (q) = {(t, x) : t \leq t_{q}, ∥ x - x_{q} ∥_{2} \leq c (t_{q} - t)} .$