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 -