  We study in this paper the sufficient conditions for enhanced continuity of
random fields, i.e. such that the modulus of its continuity allows the
factorable representation by the product of random variable on the
deterministic module of continuity.
  We estimate also the ordinary and (possible) exponential moments of these
random variables.
  We consider also the case of random fields with heavy tails of distribution
and the so-called rectangle its continuity.
