Abstract
Two examples show that certain uniform convergence properties related to the Glivenko-Cantelli theorem — properties which are known to hold in Euclidean spaces — need not hold in general Banach spaces.
This research is supported by the Danish Natural Science Research Council.
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Topsøe, F., Dudley, R.M., Hoffmann-Jørgensen, J. (1976). Two examples concerning uniform convergence of measures w.r.t. balls in Banach spaces. In: Gaenssler, P., Révész, P. (eds) Empirical Distributions and Processes. Lecture Notes in Mathematics, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096885
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DOI: https://doi.org/10.1007/BFb0096885
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