Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Geometric properties of universally measurable mappings. / Reinov, O. I.
в: Journal of Mathematical Sciences, Том 105, № 5, 2001, стр. 2436-2447.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Geometric properties of universally measurable mappings
AU - Reinov, O. I.
N1 - Funding Information: This work was partially supported by the Ministry of Education of the Russian Federation (grant No. 97-0-1.7-36) and the Federal Program “INTEGRATSIYA” (grant No. 326.532).
PY - 2001
Y1 - 2001
N2 - We study conditions under which universally measurable mappings from a separable topological space S into a metric space R (with metric ρ) belong to class D of mappings f : S → R : such that for any compact subset K ⊂ S and number ε > 0 there exists an open (in the induced topology) set V ⊂ K such that the oscillation ω(f;V) of an R-valued function f on V is less than ε (here, ω(f;V) = sups, t∈Vρ(f(s), f(t))).
AB - We study conditions under which universally measurable mappings from a separable topological space S into a metric space R (with metric ρ) belong to class D of mappings f : S → R : such that for any compact subset K ⊂ S and number ε > 0 there exists an open (in the induced topology) set V ⊂ K such that the oscillation ω(f;V) of an R-valued function f on V is less than ε (here, ω(f;V) = sups, t∈Vρ(f(s), f(t))).
UR - http://www.scopus.com/inward/record.url?scp=52549083321&partnerID=8YFLogxK
U2 - 10.1023/A:1011369314116
DO - 10.1023/A:1011369314116
M3 - Article
VL - 105
SP - 2436
EP - 2447
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 5574572