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By A. Gut, K. D. Schmidt

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Following each set universal { Fn ~ sup-norm Graves A 6 F vector a stochastic := is a n I n 6~ will U n £~ algebra "''' ~k ]) d e n o t e t h e c l a s s of a l l F - m e a s u r a b l e simple o to t h e s u p - n o r m , t h e c l a s s D o is a n M - n o r m e d its [79], completion the map characteristic measure on F D X be : F . } called basis on Fn on ~ . a stochastic ~ . Define basis on is a n function sequence on F F the , is a p a r t i t i o n Let with := of a l g e b r a s Then ~iXA.

Co. , (1967), F-processes. Proc. 5th Berkeley Symposium on Math. Stat. , Vol. l, 301-313. , (1969), Quasi-martingales. Math. Scand. 24, 79-92. , (1970), On modlfication theorems. Preprint, Arhus univ. , (1973), On a generalization of martingales due to Blake. Pacific J. Math. 48, 275-278. , (1971), A "Fatou equation" for randomly stopped variables. Ann. Math. Statist. 42, 2143-2146. Klaus D. A m a r t s a Schmidt: - m e a s u r e t h e o r e t i c a p p r o a c h I-'- ,¢ I-'- 0 C o n t e n t s I.

S. convergent semiamart that fails to be an amart, see Austin, Edgar and lonescu Tulcea (1974), page 19. E suplXnl ffi Y. 2n/P. 2-(n+l) < ~o. s. 2 shows that If p > I, then Y(P) ~ P ) "~n " n }nEN is an smart. 3. This example is related to that of Sudderth (1971), page 2145. ,n ffi I 0 otherwise and n =1,2, .... 1) x,p,C~ -~ O n Define i s now d e f i n e d a s t h e sequence Y2n ''''' ~n ' .... s. 2) Let ~k(~) ÷ 0~ X Y among T 7~ for 1 < k < n. which corresponds to the first that is non-zero and that corresponds to the last zero.

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