Abstract
Subspaces of an Orlicz space LM generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), are studied. In terms of dilations of f, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in LM. A class of Orlicz spaces such that, for all subspaces generated by independent identically distributed functions, these properties are equivalent and can be characterized by Matuszewska–Orlicz indices is determined.
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Notes
In the case \(M(u) = {{u}^{p}}\), such a subspace is also called the \(\Lambda (p)\) space.
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Funding
This research was performed at Lomonosov Moscow State University and was supported by the Russian Science Foundation, project no. 23-71-30001.
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Translated by I. Ruzanova
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Astashkin, S.V. On Subspaces of an Orlicz Space Spanned by Independent Identically Distributed Functions. Dokl. Math. 108, 297–299 (2023). https://doi.org/10.1134/S1064562423700801
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DOI: https://doi.org/10.1134/S1064562423700801