On the concept of Bernoulliness

TL;DR

This paper explores the concept of Bernoulliness by providing a natural definition of finite Bernoulli sequences, comparing it with exchangeability, and discussing historical context and formal proofs.

Contribution

It introduces a natural definition of finite Bernoulli sequences and compares it with the Kolmogorov--Martin-Lof exchangeability framework, clarifying conceptual differences.

Findings

Provides a natural definition of finite Bernoulli sequences

Analyzes the relationship between Bernoulliness and exchangeability

Includes historical background and formal proofs

Abstract

The first part of this paper is another English translation of a 1986 note. It gives a natural definition of a finite Bernoulli sequence (i.e., a typical realization of a finite sequence of binary IID trials) and compares it with the Kolmogorov--Martin-Lof definition, which is interpreted as defining exchangeable sequences. The appendix gives the historical background and proofs.