CONTENTS Introduction............................................................................................................................................................................ 5 1. Notation and preliminaries............................................................................................................................................ 5 2. Statement of the problem............................................................................................................................................... 9 3. Norming sequences....................................................................................................................................................... 11 4. A characterization of full measures belonging to $N_d(X)$.................................................................................... 16 5. A characterization of multiply ${T_t}$-decomposable probability measures on X............................................. 22 6. A reduction of the problem............................................................................................................................................. 27 7. Multiply monotone functions.......................................................................................................................................... 29 8. The Urbanik representation for d-times ${T_t}$-decomposable (d = 1,2,...) probability measures on X...... 31 9. The Urbanik representation for completely ${T_t}$-decomposable probability measures on X..................... 34 References............................................................................................................................................................................ 39
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