The central limit theorem in the space C(S) and majorizing measures (Q921700)

A new concept of majorizing measure is defined to give a sufficient condition on the CLT(p), \(1\leq p<2\), in the Banach space of continuous functions C(S). (The majorizing measure condition is weaker than the metric entropy condition given by \textit{M. B. Marcus} and \textit{G. Pisier} [Ann. Inst. Henri Poincaré, Probab. Stat. 20, 177-199 (1984; Zbl 0536.60048)].) Using the above result the author also gives a sufficient condition on the CLT(p), \(1<p<2\), in \(c_ 0\)- the Banach space of real sequences tending to zero. Also, the paper deals with some processes which have, under the majorizing measure condition, copies with continuous trajectories.