Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-08T06:29:15.640Z Has data issue: false hasContentIssue false
  • English
  • Français

Applications of convergence spaces

Published online by Cambridge University Press:  17 April 2009

Gary D. Richardson
Gary D. Richardson
Affiliation:
Department of Mathematics, East Carolina University, Greenville, North Carolina 27834, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Convergence notions are used extensively in the areas of probability and statistics. Many times proofs can be simplified by considering an appropriate convergence structure on the space and using well-known results from the theory of convergence spaces; for example, compactness arguments are sometimes simplified by using a generalized Ascoli theorem in the convergence space setting. The theory of convergence spaces is also used to generalize some results in probability and statistics.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 107 - 123
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Ash, Robert B., Real analysis and probability (Probability and Mathematical Statistics, 11. Academic Press, New York and London, 1972).Google Scholar
[2]Billingsley, Patrick, Convergence of probability measures (John Wiley & Sons, New York, London, Sydney, Toronto, 1968).Google Scholar
[3]Bourbaki, Nicolas, Elements of mathematics. General topology, Part 2 (Hermann, Paris; Addison-Wesley, Reading, Massachusetts; 1966).Google Scholar
[4]Cook, C.H. and Fischer, H.R., “On equicontinuity and continuous convergence”, Math. Ann. 159 (1965), 94–104.CrossRefGoogle Scholar
[5]Feldman, William A., “Axioms of countability and the algebra C(X)”, Pacific J. Math. 47 (1973), 81–89.CrossRefGoogle Scholar
[6]Fréchet, Maurice, “Sur quelques points du calcul fonctionnel”, Rend. Circ. Mat. Palermo 22 (1906), 1–74.CrossRefGoogle Scholar
[7]Hahn, H., Theorie der reellen Funktionen, Erster Band (J. Springer, Berlin, 1921).CrossRefGoogle Scholar
[8]Kent, D.C. and Richardson, G.D., “Minimal convergence spaces”, Trans. Amer. Math. Soc. 160 (1971), 487–499.CrossRefGoogle Scholar
[9]Lehmann, E.L., Testing statistical hypotheses (John Wiley & Sons, New York; Chapman & Hall, London; 1959).Google Scholar
[10]Loève, Michel, Probability theory, 2nd edition (Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1960).Google Scholar
[11]Novák, Josef, “On convergence spaces and their sequential envelopes”, Czechoslovak Math. J. 15 (90) (1965), 74–100.CrossRefGoogle Scholar