Geodesic
Approximation of Subspaces of Symmetric Spaces Generated by Independent Functions
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 643-652

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Let $E$ be a subspace of a symmetric space $X$ generated by $n$ independent identically distributed functions. It is proved that, under certain conditions on $X$, there exists a projection $P$, $\|P\|\le K$ ($K$ depending only on $X$) whose image contains $E$ and has dimension at most $Cn \ln(n + 1)$ ($C$ is independent of $n$ and $X$).
Keywords: uniformity function, independent functions, symmetric space, Orlicz space, Kruglov property. 
@article{MZM_2014_96_5_a0,
     author = {S. V. Astashkin},
     title = {Approximation of {Subspaces} of {Symmetric} {Spaces} {Generated} by {Independent} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--652},
     publisher = {mathdoc},
     volume = {96},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a0/}
}
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S. V. Astashkin. Approximation of Subspaces of Symmetric Spaces Generated by Independent Functions. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 643-652. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a0/