Convergence and multiplicities for the Lempert function (Q841218)

Let \(\varOmega\subset\mathbb C^n\) be a domain. The authors extend the notion of the Lempert function for \(\Omega\) to the case where poles have multiplicities given by local indicators in the sense of \textit{A. Rashkovskii} [Ann. Pol. Math. 75, No. 3, 213--231 (2000; Zbl 0966.32022)]. They prove various properties (e.g.~monotonicity, convergence) of the generalized function.