A translation of "The characteristic function of a random phenomenon" by Bruno de Finetti

TL;DR

This paper provides a precise translation of Bruno de Finetti's 1928 work on the characteristic function of a random phenomenon, clarifying original content and correcting errors for modern readers.

Contribution

It offers an accurate translation of de Finetti's foundational paper, including corrections and detailed footnotes, facilitating understanding of early probability theory.

Findings

Clarifies de Finetti's original concepts on characteristic functions

Corrects and annotates apparent mistakes in the original text

Provides context by referencing a longer version of the work

Abstract

This article is a translation of Bruno de Finetti's paper "Funzione Caratteristica di un fenomeno aleatorio" which appeared in Atti del Congresso Internazionale dei Matematici, Bologna 3-10 Settembre 1928, Tomo VI, pp. 179-190, originally published by Nicola Zanichelli Editore S.p.A. The translation was made as close as possible to the original in form and style, except for apparent mistakes found in the original document, which were corrected and are mentioned as footnotes. Most of these were resolved by comparing against a longer version of this work by de Finetti, published shortly after this one under the same titlea. The interested reader is highly encouraged to consult this other version for a more detailed treatment of the topics covered here. Footnotes regarding the translation are labeled with letters to distinguish them from de Finetti's original footnotes.