The uniform CLT for martingale difference of function-indexed process under uniformly integrable entropy (Q2717127)

The paper is concerned with the uniform central limit theorem for a process constructed from a sequence of martingale differences and indexed by a family of functions, under the assumption of uniformly integrable entropy with respect to the \(L_2\)-norm; see also \textit{J. Bae} [J. Korean Math. Soc. 32, No. 3, 427-446 (1995; Zbl 0854.60025)]. The central technique in the proof is to derive a maximal inequality for martingale difference sequences based on the Freedman inequality; see \textit{K. Ziegler} [J. Multivariate Anal. 62, No. 2, 233-272 (1997; Zbl 0895.60035)]. The main theorem weakens the conditions needed for the corresponding results in the papers cited above.