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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 изданиях › статья › Рецензирование
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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