Geodesic
On a~L.~Schwartz problem and on realization of $l_p$-spaces by spaces of random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 729-731

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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. 
@article{TVP_1969_14_4_a12,
     author = {D. Kh. Mushtari},
     title = {On {a~L.~Schwartz} problem and on realization of $l_p$-spaces by spaces of random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {729--731},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a12/}
}
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D. Kh. Mushtari. On a~L.~Schwartz problem and on realization of $l_p$-spaces by spaces of random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 729-731. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a12/