A random walk on a countable group $G$ acting metric space $X$ gives characteristic called the drift which depends only transition probability measure $\mu$ of walk. The is `translation distance' In this paper, we prove that varies continuously with measures, under assumption distance and horofunctions are expressed by certain ratios. As an example, consider mapping class $\mathrm{MCG}(S)$ Teic...

BACKGROUND The area under the receiver operating characteristic (ROC) curve, referred to as the AUC, is an appropriate measure for describing the overall accuracy of a diagnostic test or a biomarker in early phase trials without having to choose a threshold. There are many approaches for estimating the confidence interval for the AUC. However, all are relatively complicated to implement. Furthe...

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness, almost fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness on fuzzy r-minimal spa...

Several necessary and suucient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous nite fuzzy measure is equivalent to a subadditive nite fuzzy measure. A furthe...

We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem or equilibrium conditions of a stochastic equilibrium problem. We derive quantitative continuity of expected ...

Some different extensions to random sets of the most common parameters of a random variable share a common rationale: a random set represents the imprecise observation of a random variable, hence the generalized parameter contains the available information about the respective parameter of the imprecisely observed variable. Following the same principles, in this paper it is proposed a new defin...