  We prove an inequality for the entropy numbers in terms of nonlinear
Kolmogorov's widths. This inequality is in a spirit of known inequalities of
this type and it is adjusted to the form convenient in applications for
$m$-term approximations with respect to a given system. Also, we obtain upper
bounds for the $m$-term approximation by the Weak Relaxed Greedy Algorithm with
respect to a system which is not a dictionary.
