Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T03:24:00.565Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Smoothness Properties of Measures on Topological Spaces

Published online by Cambridge University Press:  20 November 2018

Shankar Hegde
Shankar Hegde*
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon, Canada
Rights & Permissions [Opens in a new window]

Abstrct

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.

V. S. Varadarajan has classified the bounded linear functional on the algebra C(X) of bounded continuous functions on a topological space X, according to the properties of their smoothness and related this classification to the corresponding natural classification of finitely additive regular measures on the zero sets of X. In this paper, some of these results are extended to the linear functionals on an arbitrary uniformly closed algebra A of bounded functions on a set X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 165 - 172
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Alexandrorff, A. D., Additive set functions in abstract spaces. Mat. Sb. (N.S.) 8(50) (1940), 307-348; 9(51) (1941), 563-628.Google Scholar
2. Dunford, N. and Schwartz, J., Linear operations, Part I. Interscience Publishers Inc., (1958).Google Scholar
3. Kirk, R. B., Algebras of bounded real valued functions. I, II. Nederl. Akad. Wetensch. Proc. Ser. A. 75 = Indag Math 34. (1972), 443-463.Google Scholar
4. Kirk, R. B. and Crenshaw, J. A., A generalized topological measure theory. Trans. Amer. Math. Soc. 207 (1975), 189-217.Google Scholar
5. Varadarajan, V. S., Measures on topological spaces. Mat. Sb. (N.S.) 55(97) (1961), 33-100, English transi., Amer. Math. Soc. Transi. (2) 48 (1965) 161-228.Google Scholar