ИСТИНА

In the Lindeberg-Feller theorem, the Lindeberg condition is present. The fulfillment of this condition must be checked for any ε>0. We formulae a new condition in terms of some generalization of moments of order 2+  , which does not depend on ε, and show that this condition is equivalent to the Lindeberg condition, and if this condition is valid for some 0   then it is valid for any >0. In the nonclassical setting (in the absence of conditions of a uniform infinitely smallness) V. I. Rotar formulated an analogue of the Lindeberg condition in terms of the second pseudo-momens. The paper presents the same modification of Rotar`s condition, which does not depend on ε. In addition, we discuss variants of the simple proofs of theorems of Lindeberg-Feller and Rotar and some related inequalities.