  We present in this paper a new sufficient condition for the so-called
Prokhorov-Skorokhod continuity of random processes. Our conditions will be
formulated in the terms of metric entropy generated by three-dimensional
distribution of the considered random process (r.p.) in the parametric set,
have a convenient and closed form, and generalize some previous results.
  We study also the conditions for weak compactness of the sequence of random
processes in this space and as a consequence the Central Limit Theorem.
  Our consideration based on the theory of Prokhorov-Skorokhod spaces of random
processes and on the theory of Banach spaces of random variables with
exponential decreasing tails of distributions, namely, on the theory of Grand
Lebesgue Spaces (GLS) of random variables.
