UNIVERSITY
OF WROC£AW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
38.2 38.1 37.2 37.1 36.2 36.1 35.2
35.1 34.2 34.1 33.2 33.1 32.2 32.1
31.2 31.1 30.2 30.1 29.2 29.1 28.2
28.1 27.2 27.1 26.2 26.1 25.2 25.1
24.2 24.1 23.2 23.1 22.2 22.1 21.2
21.1 20.2 20.1 19.2 19.1 18.2 18.1
17.2 17.1 16.2 16.1 15 14.2 14.1
13.2 13.1 12.2 12.1 11.2 11.1 10.2
10.1 9.2 9.1 8 7.2 7.1 6.2
6.1 5.2 5.1 4.2 4.1 3.2 3.1
2.2 2.1 1.2 1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 1,
pages 153 - 163
 

A CONDITION TO AVOID A PATHOLOGICAL STRUCTURE OF SUFFICIENT s -FIELDS

György Michaletzky

Abstract: Sufficiency is one of the fundamental concepts of mathematical statistic. For a statistical space (_O_, A,P) a s -field is sufficient if - roughly speaking - it contains the same information regarding the measure class P as the whole s -field A. Burkholder has constructed an example where a nonsufficient s -field is larger than a sufficient one. We show that if the Boolean algebra of equivalence classes of events is complete (where two events A, B are said to be equivalent if P (A o B) = 0 for two every measures P  (-  P ), then a sub-s -field G containing a sufficient sub-s -field F of A is sufficient iff the Boolean algebra of equivalence classes of events belonging to G is complete.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References