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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Weak convergence of the area of nonparametric $ L\sb{1}$ surfaces


Author: Kim E. Michener
Journal: Trans. Amer. Math. Soc. 234 (1977), 175-184
MSC: Primary 28A75; Secondary 49F25
MathSciNet review: 0466495
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0466495-4
PII: S 0002-9947(1977)0466495-4
Keywords: Bounded variation, surface area, vector measures, $ \mathcal{J}$-variation, distribution derivative, weak convergence
Article copyright: © Copyright 1977 American Mathematical Society