On behaviour of holomorphically contractible systems under non-monotonic sequences of sets
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The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carathéodory pseudodistances, as well as Lempert and Green functions with respect to sequences of domains converging in the Hausdorff metric are delivered.
KeywordsInvariant pseudodistances Kobayashi pseudodistance Carathéodory pseudodistance Pluricomplex Green function Hausdorff distance
Mathematics Subject ClassificationPrimary 32F45 Secondary 32H02
- 2.M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, 2nd edition, de Gruyter Expositions in Mathematrics 9, Walter de Gruyter 2014.Google Scholar
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