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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weak convergence of the area of nonparametric $L_{1}$ surfaces
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by Kim E. Michener PDF
Trans. Amer. Math. Soc. 234 (1977), 175-184 Request permission

Abstract:

The main purpose of this work is to obtain an analogue to a theorem of L. C. Young on the behavior of the nonparametric surface area of continuous functions. The analogue is for ${L^1}$ functions of generalized bounded variation. By considering arbitrary Borel vector measures and kernels other than the area kernel, results concerning the weak behavior of measures induced by a class of sublinear functionals are obtained.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 234 (1977), 175-184
  • MSC: Primary 28A75; Secondary 49F25
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0466495-4
  • MathSciNet review: 0466495