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Transactions of the American Mathematical Society

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

 
 

 

Weak convergence of the area of nonparametric $L_{1}$ surfaces


Author: Kim E. Michener
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
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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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Keywords: Bounded variation, surface area, vector measures, <!– MATH $\mathcal {J}$ –> <IMG WIDTH="23" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img4.gif" ALT="$\mathcal {J}$">-variation, distribution derivative, weak convergence
Article copyright: © Copyright 1977 American Mathematical Society