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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On upper gauge density

Authors: H. W. Pu and H. H. Pu
Journal: Proc. Amer. Math. Soc. 54 (1976), 185-188
MathSciNet review: 0390155
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Abstract: Let $ g$ be a diametric gauge over a metric space $ (X,\rho )$. It is proved, in this paper, that the upper gauge density $ D(A,x) = 0$ for almost all points of the complement of $ A$ provided that $ A$ is in a certain family which contains all Borel sets of finite measure. Also, a relation between conditions for a diametric gauge and certain regularity conditions is given.

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Additional Information

PII: S 0002-9939(1976)0390155-6
Keywords: Outer measure, upper gauge density
Article copyright: © Copyright 1976 American Mathematical Society