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On Covering Systems

Published online by Cambridge University Press:  20 November 2018

Donald J. Mallory
Affiliation:
University of British Columbia Vancouver, British Columbia
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Differentiation of a set function μ with respect to another v at a point x involves taking the limit of the ratio μA/vA as A "converges" to x in some sense which requires that A belong to some family of sets N(x) (e.g. spheres with centre x). For the development of a reasonable theory of differentiation certain restrictions must be placed on the families N(x). The best-known restriction is that they form a Vitali system. However, other systems have been considered.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Banach, S., Sur le théorème de M. Vitali, Fund. Math., 5 (1924), 134.Google Scholar
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4. Sion, M., Approximate continuity and differentiation, Can. J. Math., 14 (1962), 467476.Google Scholar