A notion of weak convergence in metric spaces
  We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar convergence is also investigated. Some applications of polar convergence follow. 
Giuseppe Devillanova, Sergio Solimini, Cyril Tintarev
math.FA