Related papers: A translation of "The characteristic function of a…
Bruno de Finetti was one of the most convinced advocates of finitely additive probabilities. The present work describes the intellectual pro- cess that led him to support that stance and provides a detailed account both of the first paper…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
This paper has been withdrawn. See quant-ph/0408115: G. M. D'Ariano, P. Perinotti and P. Lo Presti, "Classical randomness in quantum measurements"
This is a translation of Yves Benoist's "Propri\'et\'es asymptotiques des groupes lin\'eaires", Geom. and funct. anal., 7:1-47, 1997
In this work, a variant of the birth and death chain with constant intensities, originally introduced by Bruno de Finetti way back in 1957, is revisited. This fact is also underlined by the choice of the title, which is clearly a literal…
This is an English translation and digitisation of Frobenius' and Stickelberger's "On the theory of elliptic functions" first published in Journal fur die reine und angewandte Mathematik (Crelle's journal), 83, 175-179 (1877) with the title…
In 1931 de Finetti proved what is known as his Dutch Book Theorem. This result implies that the finite additivity {\it axiom} for the probability of the disjunction of two incompatible events becomes a {\it consequence} of de Finetti's…
This is a translation of Heinz Bachmann's influential paper, wherein the Bachmann-Howard ordinal is defined, and some general considerations given on systems of ordinal functions. Permission to post has been granted by the editors of…
About 160 years ago, the Italian mathematician Fa\`a di Bruno published two notes dealing about the now eponymous formula giving the derivative of any order of a composition of two functions. We reproduce here the two original notes, Fa\`a…
We provide a characterization of continuous semimartingales whose law is invariant with respect to predictable random rotations. In particular we prove that all such semimartingales are obtained by integrating a predictable process with…
The following document is a translation (from French to English) of: Gabriele H. Greco, Sur la mesurabilit\'e d'une fonction num\'erique par rapport \`a une famille d'ensembles, Rendiconti del Seminario Matematico della Universit\`a di…
This text is a commentary on the paper "On some ideals of differentiable functions" of Ren{\'e} Thom which appeared in Volume II of his "Oeuvres Math{\'e}matiques" published by the Soci{\'e}t{\'e} math{\'e}matique de France, s{\'e}rie…
This is the first translation of Hipparchus Commentaries on the Phenomena of Aratus and Eudoxus into a modern language since the one, in German, published by the philologist Karl Heinrich August Manitius in 1894. Published in 2013, it is…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
We make remarks on Fern\'{a}ndez Guasti's paper [{\it J. Phys. A: Math. Gen.} 39 (2006) 11825-11832] by pointing out some mistakes Fern\'{a}ndez Guasti derived therein.
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G., Nikonorova Yu.V. Generalized Popoviciu's problem (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 229-232 (2000), Zbl. 0958.51021. All inserted…
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of…
We give a nonstandard analytic proof of de Finetti's theorem for an exchangeable sequence of Bernoulli random variables. The theorem postulates that such a sequence is uniquely representable as a mixture of iid sequences of Bernoulli random…
We consider the class $C(T)$ of continuous real-valued functions on the circle. For certain classes of functions naturally characterised by the rapidity of decrease of Fourier coefficients we investigate whether it is possible to bring…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On a characterization of critical points of the scalar curvature functional (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 211-217 (2000), Zbl.…