Some examples of application of the metric entropy method
Using the metric entropy method, the author gives a common proof to various important tools used in establishing almost sure convergence of sequences of functions, evaluating suprema and counting up the number of occurrences of events. The author describes a unified setting suitable to prove a number of classical results, like the Rademacher-Menshov theorem, the Stechkin theorem, the Gál-Koksma theorems, the quantitative versions of Borel-Cantelli lemma. The examples concern upper and lower classes for stationary Gaussian sequences and the law of the iterated logarithm for subsequences and the Diophantine approximation relatively to Gál and Schmidt's theorems.
scientific article; zbMATH DE number 2186357
scientific article