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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Elker,J.: Unpublished "Diplomarbeit" from the Ruhr university, Bochum 1975.
Topsøe, F.: On the Glivenko-Cantelli Theorem. Z. Wahrscheinlichkeitsrechnung verw. Geb. 14, 239–250 (1970).
Topsøe, F.: Uniformity in weak convergence w.r.t. balls in Banach spaces. Math. Scand. 38, 148–158 (1976).
Vapnik, V.N., and Červonenkis, A.Ya.: On the uniform convergence of relative frequencies of events to their probabilities. Theor. Probability Appl. 16, 264–280 (1971).
Varadarajan, V.S.: On the convergence of probability distributions, Sankyã 19, 23–26 (1958).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0096885
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08061-9
Online ISBN: 978-3-540-37515-9
eBook Packages: Springer Book Archive