Invariant Probability Measures under $p$-adic Transformations
| Autor: | Morawiec, Janusz, Zürcher, Thomas |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | It is well-known that the Lebesgue measure is the unique absolutely continuous invariant probability measure under the $p$-adic transformation. The purpose of this paper is to characterize the family of all invariant probability measures under the $p$-adic transformation and to provide some description of them. In particular, we describe the subfamily of all atomic invariant measures under the $p$-adic transformation as well as the subfamily of all continuous and singular invariant probability measures under the $p$-adic transformation. Iterative functional equations play the base role in our considerations. |
| Databáze: | arXiv |
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