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Measure, Compactification and Representation

Published online by Cambridge University Press:  20 November 2018

Alan Sultan
Alan Sultan*
Affiliation:
Queens College, Flushing, New York
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The theory of measure on topological spaces has in recent years found its most natural setting in the study of pavings and measures on such pavings (see e.g. [1-3; 5; 6; 10; 19; 22; 32; 33]. In this setting the relationship between measure and topology crystallizes since one concentrates primarily on the simpler internal lattice structure associated with sublattices of the topology rather than on the more complex topological structure.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 54 - 65
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Alexandroff, A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) 8, 50 (1940), 307–348.Google Scholar
2. Alexandroff, A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) 8, 50 (1941), 563–628.Google Scholar
3. Alexandroff, A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) 13, 55 (1943), 139–268.Google Scholar
4. Alo, R. and Shapiro, H. L., Normal topological spaces (Cambridge University Press, Cambridge, Mass., 1974).Google Scholar
5. Bachman, G. and Sultan, A., Extensions of regular lattice measures with topological applications, J. Math. Anal, and Appl. 57 (1977), 539–559.Google Scholar
6. Bachman, G. and Sultan, A., Lattice regular measures: mappings and spaces, Pac. J. Math. 67 (1976), 291–321.Google Scholar
7. Banaschewski, B., Uber Nulldimensionale Raume, Math. Nach. 13 (1955), 129–140.Google Scholar
8. Biles, C. M., Gelfand and Wallman type compactifications, Pac. J. Math. 35 (1970), 267–278.Google Scholar
9. Brooks, R. M., On Wallman compactifications, Fund. Math. 60 (1967), 157–174.Google Scholar
10. Christenson, J., Topology and Borel structure, Mathematics Studies 10 (North-Holland, Amsterdam, 1974).Google Scholar
11. Dykes, N., Generalizations of realcompact spaces, Pac. J. Math. 33 (1970), 571–581.Google Scholar
12. Douglas, R. G., Banach algebra techniques in operator theory (Academic Press, New York, 1972).Google Scholar
13. Evstigneev, V., Bicompactness and measure, Funktsional’ nyl Analiz i Ego Priloztheniya 4 (1970), 51–60.Google Scholar
14. Fomin, S. and Iliadis, S., The method of centered systems in the theory of topological spaces, Uspecki Mat. Nauk 21 (1966), 47–76.Google Scholar
15. Frink, O., Compactifications and semi-normal bases, Amer. J. Math. 86 (1964), 602–607.Google Scholar
16. Gardner, R. J., The regularity of Borel measures and Borel measurecompactness, Proc. London Math. Soc. 30 (1975), 95–113.Google Scholar
17. Hager, A., Some nearly fine uniform spaces, Proc. London Math. Soc. 28 (1974), 517–546.Google Scholar
18. Hager, A., Nanzetta, P. and Plank, D., Inversion in a class of lattice ordered algebras, Colloq. Math. 24 (1972), 225–234.Google Scholar
19. Hoffman-Jorgenson, J. , The theory of analytic spaces, Math. Notes 10, Math. Inst. Aarhus University, Aarhus, Denmark (1970).Google Scholar
20. Isbell, J., Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), 96–125.Google Scholar
21. Kirk, R. B., Algebras of bounded real valued functions, I, II, Indag. Math. 31 (1969), 443–463.Google Scholar
22. Kirk, R. B. and Crenshaw, J. A., A generalized topological measure theory, Trans. Amer. Math. Soc. 207 (1975), 189–217.Google Scholar
23. Koltun, A., Measure and compactification (preprint).Google Scholar
24. Mrowka, S., Characterizations of classes of functions by Lebesgue sets, Czech. Math. J. 191 (1969), 738–748.Google Scholar
25. Mrowka, S., On some approximation theorems, Nieuw Archief voor Wiskunde 16 (1968), 94–111.Google Scholar
26. Mrowka, S., (3-like compactifications, Acta Math. Acad. Sci. Hung. 24, 279–287.Google Scholar
27. Nyikos, P. J., Not every O-dimensional realcompact space is N-compact, Bull. Amer. Math. Soc. 77 (1971), 392–396.Google Scholar
28. Rickart, J. C., Banach algebras (D. Van Nostrand, Princeton, N.J., 1960).Google Scholar
29. Steiner, E. F., Wallman spaces and compactifications, Fund. Math. 61 (1968), 295–304.Google Scholar
30. Sultan, A., General rings of functions, J. Austr. Math. Soc. 20, Series A (1975), 359–365.Google Scholar
31. Sultan, A., Hausdorff compactifications and Wallman spaces, Acta Math. Acad. Sci. Hung. 28 (3-4) (1976), 253–255.Google Scholar
32. Sultan, A., A general measure extension procedure, Proc. A.M.S. (to appear).Google Scholar
33. Topsøe, F., Topology and measure (Springer-Verlag, New York, 1970).Google Scholar
34. Varadarajan, V., Measures on topological spaces, Amer. Math. Soc. Translations, (2) 48 (1965), 161–228.Google Scholar
35. Wallman, H., Lattices and topological spaces, Ann. Math. 42 (1938), 687–697.Google Scholar