On the declared common probability space assume X_n=X almost surely for every n≥settling_index=25; inspect n=32. Give (settling_index,n,zero_probability_status,certificate?,eventual_equality_universal_tail_certificate).
G001 — On the declared common probability space assume X_n=X almost surely for every n≥settling_index=25; inspect n=32. Give (settling_index,n,zero_probability_status,certificate?,eventual_equality_universal_tail_certificate).
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
declared common probability space;X_k=X almost surely for EVERY k>=25;inspected n=32
After
inspected deviation status=0;for EVERY positive epsilon,all k>=25 have deviation probability0
Conditions: none
Use the explicitly declared all-later almost-sure equality,not a pattern guessed from this index.Earlier not_yet_zero only means the certificate has not supplied0,not a known positive probability.The all-epsilon zero tail gives the conditional convergence-in-probability certificate.
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.