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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 6, Pages 5–22 (Mi izv8468)  

On comparing systems of random variables with the Rademacher sequence

S. V. Astashkin

S. P. Korolyov Samara State Aerospace University

Abstract: We ask whether inequalities between distributions of scalar polynomials of two sequences of random variables imply that the corresponding inequalities hold between the distributions of the norms of the corresponding vector sums in an arbitrary Banach space provided that one of the systems is the Rademacher system. We show that the answer is affirmative when the Rademacher functions form the majorizing system, and negative in the opposite case.

Keywords: Rademacher functions, independent random variables, Bernoulli's conjecture, $q$-concave Banach lattice, ${\mathcal K}$-functional.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.470.2016/1.4
This paper was written while fulfilling the state request no. 1.470.2016/1.4 of the Ministry of Science and Education of Russia.


DOI: https://doi.org/10.4213/im8468

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English version:
Izvestiya: Mathematics, 2017, 81:6, 1063–1079

Bibliographic databases:

UDC: 517.5+517.982.27
MSC: 46B09, 46B20, 46B42, 46E30, 46N30, 60E15
Received: 03.11.2015
Revised: 16.05.2016

Citation: S. V. Astashkin, “On comparing systems of random variables with the Rademacher sequence”, Izv. RAN. Ser. Mat., 81:6 (2017), 5–22; Izv. Math., 81:6 (2017), 1063–1079

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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