| Autor: |
Abakumov, Evgeny, Nestoridis, Vassili, Picardello, Massimo |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Proc. Amer. Math. Soc. 2022 |
| Druh dokumentu: |
Working Paper |
| Popis: |
We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a martingale on the boundary of the tree (equipped with the harmonic measure $m$ induced by $P$) such that, for every measurable function $h$ on the boundary, it contains a subsequence that converges to $h$ in measure. Moreover, the martingale visits every open set of measurable functions with positive lower density. |
| Databáze: |
arXiv |
| Externí odkaz: |
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