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A Generalization of the Blackwell–Ryll-Nardzewski Measurable Selection Theoremстатья
- Автор: Afonin K.A.
- Журнал: Вестник Евразийского национального университета им. Л.Н.Гумилева. Серия Математика. Информатика. Механика
- Том: 134
- Номер: 1
- Год издания: 2021
- Издательство: Евразийский национальный университет имени Л.Н. Гумилева
- Местоположение издательства: Нур-Султан, Казахстан
- Первая страница: 35
- Последняя страница: 41
- Номер статьи: 3
- DOI: 10.32523/2616-678x-2020-134-1-35-41
- Аннотация: One of the main forms of the measurable selection theorem is connected with the existence of the graph of a measurable mapping in a given measurable set 𝑆 in the product of two measurable spaces 𝑋 and 𝑌 . Such a graph enables one to pick a point in the section 𝑆𝑥 for each 𝑥 in 𝑋 such that the obtained mapping will be measurable. The indicated selection is called a measurable selection of the multi-valued mapping associating to the point 𝑥 the section 𝑆𝑥 , which is a set in 𝑌 .The classical theorem of Blackwell and Ryll-Nardzewski states that a Borel set 𝑆 in the product of two complete separable metric spaces contains the graph of a Borel mapping (hence admits a Borel selection) provided that there is a transition probability on this product with positive measures for all sections of 𝑆 .The main result of this paper gives a generalization to the case where only one of the two spaces is complete separable and the other one is a general measurable space whose points parameterize a family of Borel probability measures on the first space such that the sections of the given set 𝑆 in the product have positive measures.
- Добавил в систему: Афонин Константин Александрович