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Mat. Sb., 2000, Volume 191, Number 6, Pages 3–30 (Mi msb481)  

This article is cited in 7 scientific papers (total in 7 papers)

Systems of random variables equivalent in distribution to the Rademacher system and $\mathscr K$-closed representability of Banach couples

S. V. Astashkin

Samara State University

Abstract: Necessary and sufficient conditions ensuring that one can select from a system $\{f_n\}_{n=1}^\infty$ of random variables on a probability space $(\Omega,\Sigma,\mathsf P)$ a subsystem $\{\varphi_i\}_{i=1}^\infty$ equivalent in distribution to the Rademacher system on $[0,1]$ are found. In particular, this is always possible if $\{f_n\}_{n=1}^\infty$ is a uniformly bounded orthonormal sequence. The main role in the proof is played by the connection (discovered in this paper) between the equivalence in distribution of random variables and the behaviour of the $L_p$-norms of the corresponding polynomials.
An application of the results obtained to the study of the ${\mathscr K}$-closed representability of Banach couples is presented.

DOI: https://doi.org/10.4213/sm481

Full text: PDF file (405 kB)
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English version:
Sbornik: Mathematics, 2000, 191:6, 779–807

Bibliographic databases:

UDC: 517.5+517.982
MSC: 28A20, 60E99
Received: 12.08.1999

Citation: S. V. Astashkin, “Systems of random variables equivalent in distribution to the Rademacher system and $\mathscr K$-closed representability of Banach couples”, Mat. Sb., 191:6 (2000), 3–30; Sb. Math., 191:6 (2000), 779–807

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dodds P.G., Semenov E.M., Sukochev F.A., Franchetti C., “The Banach-Saks property for function spaces”, Dokl. Math., 66:1 (2002), 91–93  mathnet  mathscinet  zmath  isi
    2. Dodds P.G., Semenov E.M., Sukochev F.A., “The Banach-Saks property in rearrangement invariant spaces”, Studia Math., 162:3 (2004), 263–294  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Astashkin S.V., Curbera G.P., “Rademacher multiplicator spaces equal to $L^\infty$”, Proc. Amer. Math. Soc., 136:10 (2008), 3493–3501  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886  mathnet  crossref  mathscinet  zmath  elib
    5. S. V. Astashkin, E. M. Semenov, “On Fourier Coefficients of Lacunary Systems”, Math. Notes, 100:4 (2016), 507–514  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Astashkin S., “Rademacher functions in weighted symmetric spaces”, Isr. J. Math., 218:1 (2017), 371–390  crossref  mathscinet  zmath  isi  scopus
    7. S. V. Astashkin, “On comparing systems of random variables with the Rademacher sequence”, Izv. Math., 81:6 (2017), 1063–1079  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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