A class of sets where convergence in Hausdorff sense and in measure coincide

Roberto Lucchetti, Fernando Sansò

Abstract


We introduce a class of uniformly bounded closed sets such that, inside the class, convergence in Hausdorff sense and in measure do agree. We also show that the class is rich enough for applications to potential theory.

Keywords


Hausdorff convergence, convergence in measure, star shaped sets

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DOI: https://doi.org/10.1478/AAPP.98S2A9

Copyright (c) 2020 Roberto Lucchetti, Fernando Sansò

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