Measurability of the banach indicatrix

We establish the measurability of the Banach indicatrix for a measurable mapping in a geometrically doubling metric space. This is a generalization of a known result for continuous transformations in Euclidean space. A system of dyadic cubes in metric space is employed to construct a sequence of measurable functions converging to the indicatrix, and we partly follow Banach’s original proof. © Instytut Matematyczny PAN, 2018.

Авторы
Evseev N. 1, 2, 3
Издательство
Institute of Mathematics. Polish Academy of Sciences
Номер выпуска
1
Язык
Английский
Страницы
97-101
Статус
Опубликовано
Том
153
Год
2018
Организации
  • 1 Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
  • 2 Novosibirsk State University, Novosibirsk, 630090, Russian Federation
  • 3 Peoples’ Friendship University of Russia, Moscow, 117198, Russian Federation
Ключевые слова
Banach indicatrix; Doubling metric space
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7114/