I.. Definition of transformed family of 6"_ fields Let us fix a probability space ( 2 ,~ ~) , an increasing right-continious family ( ~ )~o of Gfields and an adapted to this family right-continious process (~)s~o , which has the properties: 1. all paths are increasing, 2. To " 0 , L;m ~ = ~ Let ~ be the class of right-continious increasing families (~)t~o of gfields, for which all ~ are stopping times and ~ =~8 • If ~@~, there is a minimal element (~) in , defined by ~= D ~t for all ~ ~ 0 . Obviously, we can characterize properties of (~) ( specially, the structure of martingales with respect to (~t)), in terms of the family (~S). 2. Characterization of the famil~ (~) of ~fields