A Note on Convergence of Level Sets

被引：0

作者：

Camilli, F. ^{[1
]}

机构：

[1] Univ Turin, Dip Matemat, I-10123 Turin, Italy

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 1999年 / 18卷 / 01期

关键词：

Perturbed level sets; set convergence; capacity;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a sequence of functions f(n) converging in some topology to a function f, in general the 0-level set of f(n) does not give a good approximation of the one of f. In this paper we show that, if we consider an appropriate perturbation of the 0-level set of f(n), we get a sequence of sets converging to the 0-level set of f, where the type of set convergence depends on the type of convergence of f(n) to f.

引用

页码：3 / 12

页数：10

共 50 条

[21] ON THE UNIVERSAL CONVERGENCE SETS
ALTOMARE, F
ANNALI DI MATEMATICA PURA ED APPLICATA, 1984, 138 : 223 - 243
[22] SETS OF UNIFORM CONVERGENCE
PEDEMONTE, L
COLLOQUIUM MATHEMATICUM, 1975, 33 (01) : 123 - 132
[23] A note on product sets of random sets
C. Sanna
Acta Mathematica Hungarica, 2020, 162 : 76 - 83
[24] A NOTE ON PRODUCT SETS OF RANDOM SETS
Sanna, C.
ACTA MATHEMATICA HUNGARICA, 2020, 162 (01) : 76 - 83
[25] A NOTE ON RIESZ SETS AND LACUNARY SETS
BRUMMELHUIS, RGM
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1990, 48 : 57 - 65
[26] SETS OF UNIFORM CONVERGENCE AND STRONG RIESZ SETS
DRESSLER, RE
PIGNO, L
MATHEMATISCHE ANNALEN, 1974, 211 (03) : 227 - 231
[27] A note on estimation of the shape of density level sets of star-shaped distributions
Kamiya, Hidehiko
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2019, 48 (12) : 3092 - 3104
[28] CONVERGENCE OF LEVEL SETS IN TOTAL VARIATION DENOISING THROUGH VARIATIONAL CURVATURES IN UNBOUNDED DOMAINS
Iglesias, Jose A.
Mercier, Gwenael
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (02) : 1509 - 1545
[29] A note on constrained convergence
Lesnjak, G
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 325 (1-3) : 75 - 80
[30] A note on the convergence of quantizers
Hall, EB
MATHEMATICAL PROBLEMS IN ENGINEERING, 1996, 2 (01) : 57 - 61

← 1 2 3 4 5 →