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The Current Theory of Analytic Sets

Published online by Cambridge University Press:  20 November 2018

D. W. Bressler  and
M. Sion
D. W. Bressler
Affiliation:
University of British Columbia
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In this paper we describe the outlines of the theory of analytic sets from the point of view of recent work on the subject. Our aim is to present the concepts and some of the principal results in a setting useful to workers in analysis, especially those workers not familiar with the field or its current developments. No attempt has been made to include all the results concerning analytic sets—not even in a particular category. There are some excellent monographs (12; 18) as well as chapters in books (2, 8, 9, 15, 17) where the subject is treated extensively. These, however, do not contain the recent results and consider only metric spaces. Our emphasis is on a general topological setting.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 207 - 230
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Blackwell, D., On a class of probability spaces, Proc. Third Berkeley Symp. on Math. Stat. and Prob. (1954-1955) (Berkeley, 1956).Google Scholar
2. Bourbaki, N., Eléments de mathématique, VIII, Part I, vol. I l l , Topologie générale, Chapter 9 (Paris, 1958).Google Scholar
3. Braun, S., Quelques théorèmes sur les cribles boréliens, Fund. Math., 20 (1933), 166–172.Google Scholar
4. Choquet, G., Ensembles boréliens et analytiques dans les espaces topologiques, C. R. Acad. Sci. Paris, 232 (1951), 2174–2176.Google Scholar
5. Choquet, G., Theory of capacities, Ann. Inst. Fourier, Grenoble, 5 (1953-54), 131–295.Google Scholar
6. Choquet, G., Ensembles K-analytiques et K-sousliniens. Cas général et cas métriques, Ann. Inst. Fourier, £ (1959), 75-81.Google Scholar
7. Davies, R. O., Non a-finite closed subsets of analytic sets, Proc. Cambridge Phil. Soc, 52 Part 2 (1956), 174-177.Google Scholar
8. Hausdorff, F., Mengenlehre, 3rd rev. ed. (New York, 1944).Google Scholar
9. Kuratowski, C., Topologie, vol. I (Warsaw, 1952).Google Scholar
10. Lusin, N., Sur la classification de M. Baire, C. R. Acad. Sci. Paris, 164 (1917), 91–94.Google Scholar
11. Lusin, N., Sur les ensembles analytiques, Fund. Math., 10 (1928), 1–95.Google Scholar
12. Lusin, N., Leçons sur les ensembles analytiques et leurs applications (Paris, 1930).Google Scholar
13. Lusin, N. and Sierpinski, W., Sur quelques propriétés des ensembles (), Bull. Acad. Sci. Cracovie (1918), 37-48.Google Scholar
14. Lusin, N. and Sierpinski, W., Sur un ensemble non mesurable B, J. de Math., 7e sér., 2 (1923), 53–72.Google Scholar
15. Saks, S., Theory of the integral (Warsaw, 1937).Google Scholar
16. Sierpinski, W., Sur une propriété des ensembles (), Fund. Math., 8 (1926), 362.Google Scholar
17. Sierpinski, W., General topology (Toronto, 1952).Google Scholar
18. Sierpinski, W., Les ensembles projectifs et analytiques, Mém. Sci. Math, fasc, 112 (Paris, 1950).Google Scholar
19. Sion, M., On analytic sets in topological spaces, Trans. Am. Math. Soc, 96 (1960), 341–354.Google Scholar
20. Sion, M., Topological and measure theoretic properties of analytic sets, Proc. Am. Math. Soc, 11 (1960), 769–776.Google Scholar
21. Sion, M., Continuous images of B or el sets, Proc. Am. Math. Soc, 12 (1961), 385–391.Google Scholar
22. Sion, M., On capacitability and measurability, Ann. Inst. Fourier, 13 (1963), 83–99.Google Scholar
23. Sion, M. and Sjerve, D., Approximation properties of measures generated by continuous set functions, Mathematika, 9 (1962), 145–156.Google Scholar
24. Sneider, V. E., Continuous images of Suslin and Borel sets: Metrization theorems (in Russian), Dokl. Akad. Nauk SSSR (N.S.), 50 (1945), 77–79.Google Scholar
25. Sneider, V. E., Descriptive theory of sets in topological spaces (in Russian), Dokl. Akad. Nauk SSSR (N.S.), 50 (1945), 81–83.Google Scholar
26. Sneider, V. E., Descriptive theory of sets in topological spaces (in Russian), Uc. Zap. Moskov. Gos. Univ., 135, II (1948), 37–85.Google Scholar
27. Souslin, M., Sur une définition des ensembles mesurables B sans nombres transfinis, C. R. Acad. Sci. Paris, 164 (1917), 88–91.Google Scholar