A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915232749715456 |
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| author | Azouzi, Youssef Masmoudi, Marwa Watson, Bruce Alastair |
| author_facet | Azouzi, Youssef Masmoudi, Marwa Watson, Bruce Alastair |
| contents | Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the measure free setting of vector lattices (Riesz spaces). We now give a formulation of the Kakutani-Rokhlin decomposition for conditionally ergodic systems in terms of components of weak order units in a vector lattice. In addition, we prove that every aperiodic conditional expectation preserving system can be approximated by a periodic system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices Azouzi, Youssef Masmoudi, Marwa Watson, Bruce Alastair Dynamical Systems Functional Analysis 47B60, 37A30, 47A35, 60A10 Recently the Kac formula for the conditional expectation of the first recurrence time of a conditionally ergodic conditional expectation preserving system was established in the measure free setting of vector lattices (Riesz spaces). We now give a formulation of the Kakutani-Rokhlin decomposition for conditionally ergodic systems in terms of components of weak order units in a vector lattice. In addition, we prove that every aperiodic conditional expectation preserving system can be approximated by a periodic system. |
| title | A Kakutani-Rokhlin decomposition for conditionally ergodic process in the measure-free setting of vector lattices |
| topic | Dynamical Systems Functional Analysis 47B60, 37A30, 47A35, 60A10 |
| url | https://arxiv.org/abs/2403.15628 |