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

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

References

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