If X: [infinity] x [OMEGA] [right arrow] R and there exist right-continuous functions u, v: [infinity] x [OMEGA] [right arrow] R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and right-continuous functions a, b: [infinity] x [OMEGA] [right arrow] R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], then
If there exist right-continuous functions [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] such that
[X.sub.n]).sup.T], then we denote [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
We call [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] the partial B-derivatives of [X.sub.i].
Because [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], [b.sub.1] from the relation (3.2) becomes [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
If X : [infinity] x [OMEGA] [right arrow] R, then [[DELTA].sub.B] X = [D.sub.B] ([D.sub.B]X) and we denote it [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]