  For entire functions $f(z)=\sum_{n=0}^{+\infty}a_nz^n, z\in {\Bbb C},$ P.
L${\rm \acute{e}}$vy (1929) established that in the classical Wiman's
inequality $M_f(r)\leq\mu_f(r)\times $ $\times(\ln\mu_f(r))^{1/2+\varepsilon},\
\varepsilon>0,$ which holds outside a set of finite logarithmic measure, the
constant 1/2 can be replaced almost surely in some sense, by 1/4; here
  $M_f(r)=\max\{|f(z)|\colon |z|=r\},\ \mu_f(r)=\max\{|a_n|r^n\colon n\geq0\},\
r>0. $ In this paper we prove that the phenomenon discovered by P.
L${\rm\acute{e}}$vy holds also in the case of Wiman's inequality for entire
functions of several variables, which gives an affirmative answer to the
question of A. A. Goldberg and M. M. Sheremeta (1996) on the possibility of
this phenomenon.
