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For $\,0<\alpha\le \infty$, new subclasses $\,\mathcal{U}^{<\alpha>}$ of theclass $\,\mathcal{U}$, of s-selfdecomposable probability measures, are studied.They are described by random integrals, by their characteristic functions andtheir L\'evy spectral measures. Also their relations with the classical L\'evyclass $L$ of selfdecomposable distributions are investigated.

The random integral representation hypothesis revisited : new classes of s-selfdecomposable laws