Rezumat articol ediţie STUDIA UNIVERSITATIS BABEŞ-BOLYAI

În partea de jos este prezentat rezumatul articolului selectat. Pentru revenire la cuprinsul ediţiei din care face parte acest articol, se accesează linkul din titlu. Pentru vizualizarea tuturor articolelor din arhivă la care este autor/coautor unul din autorii de mai jos, se accesează linkul din numele autorului.

 
       
         
    STUDIA MATHEMATICA - Ediţia nr.3 din 2007  
         
  Articol:   COMPLETENESS WITH RESPECT TO THE PROBABILISTIC POMPEIU-HAUSDORFF METRIC.

Autori:  ŞTEFAN COBZAŞ.
 
       
         
  Rezumat:  The aim of the present paper is to prove that the family of all closed nonempty subsets of a complete probabilistic metric space L is complete with respect to the probabilistic Pompeiu-Hausdorff metric H. The same is true for the families of all closed bounded, respectively compact, nonempty subsets of L. If L is a complete random normed space in the sense of Šerstnev, then the family of all nonempty closed convex subsets of L is also complete with respect to H. The probabilistic Pompeiu-Hausdorff metric was defined and studied by R.J. Egbert, Pacific J. Math. 24 (1968), 437-455, in the case of Menger probabilistic metric spaces, and by R.M. Tardiff, Pacific J. Math. 65 (1976), 233-251, in general probabilistic metric spaces. The completeness with respect to probabilistic Pompeiu-Hausdorff metric of the space of all closed bounded nonempty subsets of some Menger probabilistic metric spaces was proved by J. Kolumbán and A. Soós, Studia Univ. Babes-Bolyai, Mathematica, 43 (1998), no. 2, 39-48, and 46 (2001), no. 3, 49-66.  
         
     
         
         
      Revenire la pagina precedentă