  We derive the exponential as well as power decreasing tail estimations for
normed sums of centered independent identical distributed (or not) random
variables on the Khintchine's form. We consider arbitrary, in particular,
non-Rademacher's variables and not only Lebesgue-Riesz rearrangement invariant
norms for the random variables. We intend to calculate the value of
correspondent limit.
