Weak convergence of the area of nonparametric 𝐿₁ surfaces

Michener, Kim E.

doi:10.1090/S0002-9947-1977-0466495-4

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

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