Use complete qualified finite source and target sigma-algebras. Each subset has sorted distinct carrier labels; the duplicate-free family is already ordered by increasing bit mask. Check preimages of target measurable sets, not images of source sets. Measurable does not mean continuous, integrable or measure-preserving. source size=6, source sigma=[[], [0, 1, 4], [2, 3, 5], [0, 1, 2, 3, 4, 5]], event=[0] normalized as a set. The indicator maps members to 1 and others to 0, with the full measurable structure on {0,1}. Give (source size,event,complete indicator mapping,event is source-measurable?).
G001 — Use complete qualified finite source and target sigma-algebras. Each subset has sorted distinct carrier labels; the duplicate-free family is already ordered by increasing bit mask. Check preimages of target measurable sets, not images of source sets. Measurable does not mean continuous, integrable or measure-preserving. source size=6, source sigma=[[], [0, 1, 4], [2, 3, 5], [0, 1, 2, 3, 4, 5]], event=[0] normalized as a set. The indicator maps members to 1 and others to 0, with the full measurable structure on {0,1}. Give (source size,event,complete indicator mapping,event is source-measurable?).
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.
Qualify the complete bit-mask-ordered family:empty set,universe,complements and all pair unions.In a finite family a countable union has only finitely many distinct members,so finite-union closure suffices.
The four target preimages are empty,event complement,event,and universe.The qualified source sigma contains empty/universe and is complement-closed,so indicator measurability is equivalent to event measurability.
S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
Result
(6, [0], [1, 0, 0, 0, 0, 0], No)
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.