A general multiparameter version of Gnedenko's transfer theorem

TL;DR

This paper introduces a comprehensive transfer theorem for random variables in metric spaces with random multiparameters, extending Gnedenko's classical results to a more general setting.

Contribution

It generalizes transfer theorems to multiparameter random variables in metric spaces, broadening the scope of classical results.

Findings

Provides a unifying principle for transfer theorems

Extends classical results to multiparameter and metric space settings

Offers a widely applicable framework for limit theorems

Abstract

Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by Gnedenko. We present a widely applicable transfer theorem for random variables on a general metric space with random multiparameters instead of random sample sizes. This summarizes an intrinsic principle behind the transfer type results known from the literature.