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The method of \emph{random integral representation}, that is, the method ofrepresenting a given probability measure as the probability distribution ofsome random integral, was quite successful in the past few decades. In thisnote we will find such a representation for generalized s-selfdecomposable andselfdecomposable distributions that have the \emph{factorization property}.These are the classes $\mathcal{U}^f_{\be}$ and $L^f$, respectively.

Factorization Property of Generalized s-self-decomposable measures and class $L^f$ distributions