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On an inequality of A. Ya. Khinchin. (Russian) Zbl 0568.60015
Problems of stability of stochastic models, Proc. Semin., Moskva 1984, 92-94 (1984).
[For the entire collection see Zbl 0554.00006.]
A classical inequality of Khinchin states that the $$L^ s$$ norm $$(1\leq s<\infty)$$ of $$\sum^{n}_{k=1}c_ kr_ k$$, where $$\{r_ k\}$$ is the system of Rademacher functions, $$n\in N$$ and $$c_ 1,c_ 2,...,c_ n\in R$$, has a lower and upper bound of the form $$C_ s(\sum^{n}_{k=1}c^ 2_ k)^{1/2}$$. The author generalizes this property for sequences of symmetric rv’s $$\{r_ k\}$$ and for more general Banach space norms $$(L^ s$$ is replaced by a symmetric Banach space of measurable functions on [0,1] such that this Banach space is an interpolation between $$L^ 1$$ and $$L^{\infty})$$.
Reviewer: G.J.Székely

##### MSC:
 60E15 Inequalities; stochastic orderings 60B05 Probability measures on topological spaces