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On Iterated Limits of Measurable Mappings

Published online by Cambridge University Press:  20 November 2018

Elias Zakon
Elias Zakon*
Affiliation:
University of Windsor, Summer Research Institute of the Canadian Math. Congress
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Egoroff' s theorem [1] was extended by Kvačko [3] to functions with values in a separable metric space; and, as is easily seen, this result applies also to separable pseudometric spaces. In the present note we shall use this theorem to obtain some propositions on iterated limits, which, despite their simplicity, seem not yet to be known in the proposed generality.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 83 - 91
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Egoroff, D. T., Sur les suites de fonctions mesurables, C.R. Acad. Sci. Paris, 152(1911), 244-6.Google Scholar
2. Kelley, J., General Topology, D. Van Nostrand, N. Y., 1960.Google Scholar
3. Kvačko, M. E., On measurable mappings of spaces (Russian, English summary), Vestnik Leningr. Univ. 13(1958), no. 13, 87-101. (Quoted in Math. Reviews, 1959, no. 5267, p. 873).Google Scholar
4. Tolstov, G., Une remarque sur le théorème de D. Th. Egoroff, Doklady Acad. Nauk SSSR (N. S.) 60 (1948), 973-5.Google Scholar
5. Weston, J. D., A counterexample concerning Egoroff' s theorem, J. London Math. Soc. 34(1959), 139-140.Google Scholar
6. Zakon, E., On, "essentially metrizable" spaces and on measurable functions with values in such spaces, (to appear in the Transactions, Am. Math. Society).Google Scholar