$p$-extremal length and $p$-measurable curve families
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- by Joseph Hesse
- Proc. Amer. Math. Soc. 53 (1975), 356-360
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385052-5
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Abstract:
It is well known that the reciprocal of $p$-extremal length, considered as a set function, is an outer measure. We show that if a curve family in euclidean $n$-space is measurable with respect to this outer measure, then the $p$-extremal length of the curve family is zero or infinite.References
- Bent Fuglede, Extremal length and functional completion, Acta Math. 98 (1957), 171–219. MR 97720, DOI 10.1007/BF02404474
- H. Renggli, Extremallängen und eine konform invariante Massfunktion für Kurvenscharen, Comment. Math. Helv. 41 (1966/67), 10–17 (German). MR 204650, DOI 10.1007/BF02566865 J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., vol. 229, Springer-Verlag, Berlin and New York, 1971.
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 356-360
- MSC: Primary 28A10; Secondary 30A44, 31B15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0385052-5
- MathSciNet review: 0385052