A CONDITION TO AVOID A PATHOLOGICAL STRUCTURE OFSUFFICIENT-FIELDS

György Michaletzky

Abstract: Sufficiency is one of the fundamental concepts of mathematical statistic. For a
statistical space a -field is sufficient if - roughly speaking - it contains the same
information regarding the measure class as the whole -field Burkholder has
constructed an example where a nonsufficient -field is larger than a sufficient one. We
show that if the Boolean algebra of equivalence classes of events is complete (where two
events are said to be if for two every measures
), then a sub--field containing a sufficient sub--field of is sufficient
iff the Boolean algebra of equivalence classes of events belonging to is complete.