A new proof of the Komlós-Révész-theorem
If r.v.s \(\{X_ n\}\) are given satisfying the moment boundedness condition E \(| X_ n| \leq 1\) then there exists a subsequence \(\bar X_ n=X_{n_ k}\) and a r.v. X with E \(| X| \leq 1\) such that \(n^{-1}\sum^{n}_{i=1}\bar X_ i\to^{a.s.}X.\) This statement has been proved by \textit{P. Révész} [Acta Math. Acad. Sci. Hungar. 16, 311-318 (1965; Zbl 0203.195)] and also by \textit{J. Kolmós} [ibid. 18, 217-229 (1967)]. The author gives a new and simpler proof using some ideas of the theory of orthogonal series and the truncation technique.
scientific article; zbMATH DE number 4149254