Sur une inégalité de H. P. Rosenthal et le théorème limite central dans les espaces de Banach (Q1064649)

The author uses the \textit{J. Zinn} [see Probability in Banach spaces III, Proc. 3rd int. Conf., Medford/USA 1980, Lect. Notes Math. 860, 324-329 (1981; Zbl 0482.60009)] reformulation of the \textit{H. P. Rosenthal} [ibid. 8, 273-303 (1970; Zbl 0213.193) and Proc. 6th Berkeley Sympos. math. Statist. Probab., Univ. Calif. 1970, 2, 149-167 (1972; Zbl 0255.60003)] generalisation of Khintchine inequalities to study the central limit theorem in Banach spaces. He proves that the validity of the Rosenthal- Zinn inequality characterizes the spaces for which the classical necessary conditions to the CLT are also sufficient ones.