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The approximate local monotony of measurable functions

Published online by Cambridge University Press:  24 October 2008

I. J. Good
I. J. Good
Affiliation:
Jesus CollegeCambridge
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Extract

1. The description “approximate”, as applied to properties of a measurable function at a point, has come to mean, roughly speaking, “with the neglect of sets of measure zero”. If a function has, at a point x0, a certain property, such as differentiability or continuity, then it has the same property in the approximate sense, but not conversely.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 1 , January 1940 , pp. 9 - 13
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

REFERENCES

(1)Saks, . Theory of the integral (Warsaw, 1937), p. 295.Google Scholar
(2)Khintchine, . “Recherches sur la structure des fonctions mesurables.” Rec. Math. Soc. Moscou, 31 (1924), 265–85.Google Scholar
(3) Saks. Loc. cit. p. 277.Google Scholar

See also

Khintchine, . “Recherches sur la structure des fonctions mesurables.” Rec. Math. Soc. Moscou, 31 (1924), 377–433; Fundam. Math. 9 (1927), 212–79.Google Scholar
Denjoy, . “Mémoire sur la totalisation des nombres dérivés non-sommables.” Ann. Ecole Norm. 33 (1916), 127–222 (209).Google Scholar
Banach, . “Sur une classe de fonctions continues.” Fundam. Math. 8 (1926), 166–73.CrossRefGoogle Scholar