Convergence of Triangular Transformations of Measures
| Autor: | D. E. Alexandrova |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Discrete mathematics Mathematics::Logic Metrization theorem Product (mathematics) Convergence (routing) Mathematics::General Topology Countable set Mathematics::Spectral Theory Statistics Probability and Uncertainty Borel probability measure Measure (mathematics) Mathematics |
| Zdroj: | Theory of Probability & Its Applications. 50:113-118 |
| ISSN: | 1095-7219 0040-585X |
| Popis: | We prove that if a Borel probability measure $\mu$ on a countable product of Souslin spaces satisfies a certain condition of atomlessness, then for every Borel probability measure $\nu$ on this product, there exists a triangular mapping $T_{\mu,\nu}$ that takes $\mu$ to $\nu$. It is shown that in the case of metrizable spaces one can choose triangular mappings in such a way that convergence in variation of measures $\mu_n$ to $\mu$ and of measures $\nu_n$ to $\nu$ implies convergence of the mappings $T_{\mu_n,\nu_n}$ to $T_{\mu,\nu}$ in measure $\mu$. |
| Databáze: | OpenAIRE |
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