In this paper, the relationships between metric spaces and $g$-metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, ε-optimal solutions are considered. The setup is illustrated on consistency of a ε-M
-estimator in linear regression model.