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In 1961 B. S. Mityagin posed a problem to give a characterization of the extension property of compact sets in geometric terms.We show that there is no such characterization in terms of Hausdorff measures or densities of measures or Hausdorff contents. This is similar to the situation in Potential Theory where R. Nevanlinna and H. Ursell proved that there is no general geometric characterization of polarity of compact sets. Tea and cookies will be served before the seminar.