This is an announcement for the paper "Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces" by F. Sukochev and D. Zanin. Abstract: \begin{abstract} {\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $0<q<1$ for which $ \Vert \sum_{_{k=1}}^n\xi_k\Vert _{E}\leq Cn^{q}$, where $\{\xi_k\}_{k\ge 1}\subset E$ is an arbitrary sequence of independent identically distributed symmetric random variables on $[0,1]$ and $C>0$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces. \end{abstract} Archive classification: math.FA Mathematics Subject Classification: 46E30 (46B09 46B20) Citation: Studia Math. 191 (2009), no. 2, 101--122 The source file(s), sukochev_zanin_submitted.tex: 67832 bytes, is(are) stored in gzipped form as 1001.2432.gz with size 20kb. The corresponding postcript file has gzipped size 84kb. Submitted from: zani0005@csem.flinders.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.2432 or http://arXiv.org/abs/1001.2432 or by email in unzipped form by transmitting an empty message with subject line uget 1001.2432 or in gzipped form by using subject line get 1001.2432 to: math@arXiv.org.