### 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. The CLT proved

here is obtained by establishing the near equivalence of standardized averages

obtained from L2 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.

sense of Nelson’s Radically Elementary Probability Theory. The CLT proved

here is obtained by establishing the near equivalence of standardized averages

obtained from L2 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.

#### Full Text:

3. [PDF]DOI: https://doi.org/10.4115/jla.2015.7.3

This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Logic and Analysis ISSN: 1759-9008