  We obtain some sufficient conditions for the Central Limit Theorem for the
random processes (fields) with values in the separable part of Holder space in
the modern terms of majorizing (minorizing) measures, belonging to X.Fernique
and M.Talagrand.
  We introduce a new class of Banach spaces-rectangle Holder spaces and
investigate CLT in this spaces via the fractional order Sobolev-Grand Lebesgue
norms.
  Our further considerations based on the improvement of the L.Arnold and
P.Imkeller generalization of the classical Garsia-Rodemich-Rumsey inequality,
which allow us to reduce degree of the distance in the important particular
cases.
