Near equivalence on metric spaces and a nonstandard central limit theorem

Abstract

This article proves a nonstandard Central Limit Theorem (CLT) in the sense of Nelson's Radically Elementary Probability Theory [11]. The CLT proved here is obtained by establishing the near equivalence of standardized averages obtained from L 2 IID random variables to the standardized average resulting from a binomial CLT. A nonstandard model for near equivalence on metric spaces replaces conventional results of weak convergence. Statements and proofs remain radically elementary without applying the full Internal Set Theory. A nonstandard notion of normality is discussed.2010 Mathematics Subject Classification 60F05 (primary); 60F25, 03H05 (secondary)