Laws of large numbers for classes of functions
Glivenko-Cantelli theorems are proved for the sequence of empirical measures corresponding to a sequence of independent and identically distributed random elements in a measurable space when these measures are indexed by classes of complex valued functions. The conditions are expressed in terms of metric entropy. The general results are applied to get uniform rate results for kernel density estimators and for empirical characteristic functions.
scientific article; zbMATH DE number 3915315