Universal and complete sets in martingale theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390812" target="_blank" >RIV/00216208:11320/18:10390812 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/malq.201500094" target="_blank" >https://doi.org/10.1002/malq.201500094</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/malq.201500094" target="_blank" >10.1002/malq.201500094</a>

Result language
angličtina
Original language name
Universal and complete sets in martingale theory
Original language description
The Doob convergence theorem implies that the set of divergence of any martingale has measure zero. We prove that, conversely, any G(delta sigma) subset of the Cantor space with Lebesgue-measure zero can be represented as the set of divergence of some martingale. In fact, this is effective and uniform. A consequence of this is that the set of everywhere converging martingales is Pi(1)(1)-complete, in a uniform way. We derive from this some universal and complete sets for the whole projective hierarchy, via a general method. We provide some other complete sets for the classes Pi(1)(1) and Sigma(1)(2) in the theory of martingales.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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