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An Alberti's rank-one
theorem for martingales
Rami Ayoush, Dmitriy Stolyarov and Michał Wojciechowski |
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Vol. 334 (2025), No. 1, 1–11
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Abstract |
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We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the -regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti’s rank-one theorem. |
Keywords
vector measure, martingale, rank-one property
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Mathematical Subject Classification
Primary: 28B05, 60G46
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Milestones
Received: 30 July 2023
Revised: 6 November 2024
Accepted: 22 December 2024
Published: 30 December 2024
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Authors |
| Rami Ayoush | |
| Institute of Mathematics University of Warsaw 02-097 Warsaw Poland |
Institute of Analysis Johannes Kepler Universität Linz A-4040 Linz Austria |
| Dmitriy Stolyarov | |
| Department of Mathematics and
Computer Sciences St. Petersburg State University St. Petersburg 199178 Russia |
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| Michał Wojciechowski | |
| Institute of Mathematics Polish Academy of Sciences 00-656 Warsaw Poland |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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