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Measurability of the banach indicatrix. / Evseev, Nikita.

в: Colloquium Mathematicum, Том 153, № 1, 01.01.2018, стр. 97-101.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Evseev, N 2018, 'Measurability of the banach indicatrix', Colloquium Mathematicum, Том. 153, № 1, стр. 97-101. https://doi.org/10.4064/cm6881-7-2017

APA

Vancouver

Evseev N. Measurability of the banach indicatrix. Colloquium Mathematicum. 2018 янв. 1;153(1):97-101. doi: 10.4064/cm6881-7-2017

Author

Evseev, Nikita. / Measurability of the banach indicatrix. в: Colloquium Mathematicum. 2018 ; Том 153, № 1. стр. 97-101.

BibTeX

@article{4201ce29c7504e89a317a4aa67f2863f,
title = "Measurability of the banach indicatrix",
abstract = "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{\textquoteright}s original proof.",
keywords = "Banach indicatrix, Doubling metric space",
author = "Nikita Evseev",
year = "2018",
month = jan,
day = "1",
doi = "10.4064/cm6881-7-2017",
language = "English",
volume = "153",
pages = "97--101",
journal = "Colloquium Mathematicum",
issn = "0010-1354",
publisher = "Institute of Mathematics, Polish Academy of Sciences",
number = "1",

}

RIS

TY - JOUR

T1 - Measurability of the banach indicatrix

AU - Evseev, Nikita

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Banach indicatrix

KW - Doubling metric space

UR - http://www.scopus.com/inward/record.url?scp=85048686880&partnerID=8YFLogxK

U2 - 10.4064/cm6881-7-2017

DO - 10.4064/cm6881-7-2017

M3 - Article

AN - SCOPUS:85048686880

VL - 153

SP - 97

EP - 101

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

SN - 0010-1354

IS - 1

ER -

ID: 14103183