On upper gauge density
HTML articles powered by AMS MathViewer
- by H. W. Pu and H. H. Pu PDF
- Proc. Amer. Math. Soc. 54 (1976), 185-188 Request permission
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.References
- W. Eames, A local property of measurable sets, Canadian J. Math. 12 (1960), 632–640. MR 122954, DOI 10.4153/CJM-1960-057-8
- Gerald Freilich, Gauges and their densities, Trans. Amer. Math. Soc. 122 (1966), 153–162. MR 206197, DOI 10.1090/S0002-9947-1966-0206197-5
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 185-188
- DOI: https://doi.org/10.1090/S0002-9939-1976-0390155-6
- MathSciNet review: 0390155