A probabilistic version of Rosenthal’s inequality

@inproceedings{Astashkin2013APV,
  title={A probabilistic version of Rosenthal’s inequality},
  author={Sergey V. Astashkin and Konstantin E. Tikhomirov},
  year={2013}
}
k=1 m{t ∈ [0, 1] : |fk(t)| > τ} (τ > 0), where m is the Lebesgue measure. Let F ∗(t) be the non-increasing left-continuous rearrangement of F (t) and, as usual, χA be the characteristic function of a set A. In [1, Theorem 1], Johnson and Schechtman proved that for every quasi-normed rearrangement invariant (r.i.) space X on [0, 1] and for the arbitrary sequence {fk}k=1 ⊂ X (n ∈ N) of non-negative independent functions, the following inequality holds: 
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