Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-31T08:48:57.013Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on the Theorems of Lusin and Egoroff

Published online by Cambridge University Press:  20 November 2018

Elias Zakon
Elias Zakon*
Affiliation:
University of Windsor
Rights & Permissions [Opens in a new window]

Extract

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.

In this note we do not intend to establish new results but only to suggest avery simple proof of Lusin's theorem, direct for σ-finite regular measures,a proof that bypasses the usual procedure of first establishing this theoremfor sets of finite measure only. The proposed proof utilizes the notion ofsubuniform convergence, a method which seems not yet to have been used,despite its simplicity and adaptability. Simultaneously, a useful supplementto Egoroff's theorem will be obtained.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 291 - 295
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Egoroff, D. T., Sur les suites des fonctions mesurables, C.R. Acad. Sci. Paris, 152(1911), 244–246.Google Scholar
2. Halmos, P. R., Measure Theory, D. Van Nostrand, N.Y., 1950.Google Scholar
3. Lusin, N., Sur les propriétés des fonctions mesurables, C.R. Acad. Sci. Paris, 154(1912), 1688–1690.Google Scholar
4. Munroe, M. E., Introduction to Measure and Integration, Addison-Wesley, Reading, Mass., 1959.Google Scholar
5. Saks, S., Theory of the Integral, Hafner, N.Y., 1937.Google Scholar
6. Schaerf, H. M., On the continuity of measurable functions in neighborhood spaces, Portug. Mathem., (1947), 33–44.Google Scholar
7. Schaerf, H. M., Dtto (II), ibid., (1948), 91–92.Google Scholar
8. Kelley, J., General Topology, Van Nostrand, 1960.Google Scholar