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For $\,0 }$ of the class $\,\mathcal{U}$, of s-selfdecomposable probability measures, are studied. They are described by random integrals, by their characteristic functions and their L\'evy spectral measures. Also their relations with the classical L\'evy class $L$ of selfdecomposable distributions are investigated.

THE RANDOM INTEGRAL REPRESENTATION HYPOTHESIS REVISITED: NEW CLASSES OF S-SELFDE.COMPOSABLE LAWS