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On Strong Upper Densities

Published online by Cambridge University Press:  20 November 2018

W. Eames
W. Eames*
Affiliation:
Lakehead University Port Arthur
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Let ψ be the outer measure generated by a gauge g and a sequential covering class C of closed sets of a metric space X, and let D be the resulting strong upper density function. That is, for each A ⊆ X and each x ∈ X:

the infimum being taken over all countable subcollections {Iα} of C such that and, for all Iα in the subcollection, d(Iα) < ε where d(Iα) is the diameter of d(Iα).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969, pp. 509 - 510
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Eames, W., A local property of measurable sets. Canad. J. Math. 12 (1960) 632–640.Google Scholar
2. Freilich, G., Gauges and their densities. Trans. Amer. Math. Soc. 122 (1966) 153–162.Google Scholar