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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

$p$-extremal length and $p$-measurable curve families
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by Joseph Hesse PDF
Proc. Amer. Math. Soc. 53 (1975), 356-360 Request permission

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.
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Additional 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