On a L. Schwartz problem and on realization of $l_p$-spaces by spaces of random variables

Urbanyk and Woyczinski have shown that $l_p$-spaces, $p\le2$, may be realized by spaces of random variables [1]. In the present paper, we prove that such realization is impossible for $l_p$-spaces with $p>2$ and for $c_0$-space.
We prove also the L. Schwartz hypothesis: if the series $X_n$ of random variables diverges in measure then there exists a sequence $\{\alpha_n\}\in R$ with $\lim\alpha_n=0$ such that $\Sigma\alpha_nX_n$ diverges in measure.