No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
107 Letters from Paul Lévy to Maurice Fréchet
Abstract
The second part contains the transcription of the 107 letters from Paul Lévy to Maurice Fréchet sent between 1918 and 1965, which are now kept at Paris Academy of Science. The original French text of the letters is annotated by numerous footnotes giving explanations on names, events, references and so on.
... 1.1936) that probability involving an infinite sequence of random variables can only be understood through finite approximation. See Barbut et al. (2004). ...
The historical background of first countable additivity, and then finite additivity, in probability theory is reviewed. We discuss the work of the most prominent advocate of finite additivity, de Finetti, and also the work of Savage. Both were most noted for their contributions to statistics; our focus here is more from the point of view of probability theory. The problem of measure is then discussed - the possibility of extending a measure to all subsets of a probability space. The theory of gambling is discussed next, as a test case for the relative merits of finite and countable additivity. We then turn to coherence of decision making, where a third candidate presents itself - non-additivity. We next consider the impact of different choices of set-theoretic axioms.
Argument
The Germans occupying Paris arrested Emile Borel and three other members of the Académie des Sciences in October 1941 and released them about five weeks later. Drawing on German and French archives and other sources, we argue that these events illustrate the complexity of the motivations and tactics of the occupiers and the occupied. While Borel and his colleagues were genuine members of the Resistance, and those who arrested them were full participants in a brutal occupation, both sides respected a bargain, of no small importance to the Vichy regime, that allowed the university to pursue its work if its members avoided overt acts of opposition.
In the present paper, we consider how Paul Lévy used martingale-type conditions for his studies on sums of dependent random variables during the 1930s. In a second part, we study L’evy’s troubled relationship with Jean-André Ville and his disdain for Ville’s mathematical work.
The present paper deals with the life and some aspects of the scientific
contributions of the mathematician Ren\'e Gateaux, killed during World War 1 at
the age of 25. Though he died very young, he left interesting results in
functional analysis. In particular, he was among the first to try to construct
an integral over an infinite dimensional space. His ideas were extensively
developed later by Paul L\'evy. Among other things, L\'evy interpreted
Gateaux's integral in a probabilistic framework that later contributed to the
construction of the Wiener measure. This article tries to explain this singular
personal and professional destiny in pre- and postwar France.
We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.
Jean André Ville (1910–1989), who brought the concept of a martingale into the mathematical theory of probability, is relatively little known. This article recounts circumstances and events of the first three decades of his life, from his birth in Marseille on June 24, 1910, to his defense of a doctoral thesis in 1939, on the eve of World War II. Additional information about his life and work is provided in other articles and documents in this issue of the Electronic Journal for History of Probability and Statistics.
Andrei Kolmogorov’s Grundbegriffe der Wahrscheinlichkeits-rechnung put probability’s modern mathematical formalism in place. It also provided a philosophy of probability—an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two aspects of the Grundbegriffe—the work of the earlier scholars whose ideas Kolmogorov synthesized.
L’histoire d’une politique des inventions 1887–1918. Cahiers pour l’histoire du CNRS
- Y Roussel
Quelques aspects de la pensée d’un mathématicien
- P Lévy
Œuvres, éditées sous sa direction par D. Dugué, avec la collaboration de P
- P Lévy
The ghosts of the ecole normale, life, death and destiny of René Gateaux (to appear)
- L Mazliak
L’histoire d’une politique des inventions 1887-1918. Cahiers pour l’histoire du CNRS 1939-1989
- Y Roussel
Paul Lévy: la période de guerre
- B Locker