Alberti's type rank one theorem for martingales
| Autor: | Ayoush, Rami, Stolyarov, Dmitriy, Wojciechowski, Michał |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the $q$-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. Comment: 10 pages |
| Databáze: | arXiv |
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