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The Splendors and Miseries of MartingalesCounterexamples to Abstract Probability: Ten Letters by Jessen, Doob and Dieudonné

The Splendors and Miseries of Martingales: Counterexamples to Abstract Probability: Ten Letters... [These ten letters are mainly about two erroneous theorems published by Joseph Doob in 1938. Both concerned probability measures on abstract spaces. The first concerned the construction of measures on infinite-dimensional product spaces from their finite-dimensional margins (the Daniell-Kolmogorov construction). The second concerned the existence of regular conditional probabilities. Ten years after the theorems were published and used by Doob’s students, counterexamples were independently discovered by Jean Dieudonné and by Erik Sparre Andersen in collaboration with Børge Jessen. The correspondence begins when Jessen writes to Doob about the counterexample he and Sparre Andersen had discovered. It reveals that Doob had not encountered Jessen’s theorem until then, and it suggests that Doob’s return to martingales, which he had left aside after his initial work on them in 1940, was inspired by his learning about Jessen’s work on the topic.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesCounterexamples to Abstract Probability: Ten Letters by Jessen, Doob and Dieudonné

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn

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References (13)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
361 –373
DOI
10.1007/978-3-031-05988-9_16
Publisher site
See Chapter on Publisher Site

Abstract

[These ten letters are mainly about two erroneous theorems published by Joseph Doob in 1938. Both concerned probability measures on abstract spaces. The first concerned the construction of measures on infinite-dimensional product spaces from their finite-dimensional margins (the Daniell-Kolmogorov construction). The second concerned the existence of regular conditional probabilities. Ten years after the theorems were published and used by Doob’s students, counterexamples were independently discovered by Jean Dieudonné and by Erik Sparre Andersen in collaboration with Børge Jessen. The correspondence begins when Jessen writes to Doob about the counterexample he and Sparre Andersen had discovered. It reveals that Doob had not encountered Jessen’s theorem until then, and it suggests that Doob’s return to martingales, which he had left aside after his initial work on them in 1940, was inspired by his learning about Jessen’s work on the topic.]

Published: Oct 18, 2022

Keywords: Børge Jessen; Daniell-Kolmogorov theorem; Disintegration of probability measures; Erik Sparre Andersen; History of probability; Jean Dieudonné; Joseph Doob; Martingales

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