This is an announcement for the paper "Tchebyshev's characteristic of rearrangement invariant space" by E.Ostrovsky and L.Sirota. Abstract: We introduce and investigate in this short article a new characteristic of rearrangement invariant (r.i.) (symmetric) space, namely so-called Tchebychev's characteristic. We reveal an important class of the r.i. spaces - so called regular r. i. spaces and show that the majority of known r.i. spaces: Lebesgue-Riesz, Grand Lebesgue Spaces, Orlicz, Lorentz and Marcinkiewicz r.i. spaces are regular. But we construct after several examples of r.i. spaces without the regular property. Archive classification: math.FA Submitted from: leos@post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1208.2393 or http://arXiv.org/abs/1208.2393