Lévy‘s and Feller‘s theorems of 1935 served as a paradigm for further work on sums of independent one- or multidimensional random variables, on the one hand. This strand of development largely preserved the “traditional” analytic orientation. On the other hand, generalizations toward martingales and random elements in metric spaces triggered a growing influence of measure theory even on the “classical” limit problems of probability.
KeywordsCharacteristic Function Limit Theorem Independent Random Variable Random Element Invariance Principle
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