The M-components of level sets of continuous functions in WBV.

Título inglés The M-components of level sets of continuous functions in WBV.
Título español Los M-componentes de conjuntos de nivel de funciones continuas en WBV.
Autor/es Ballester, Coloma ; Caselles, Vicent
Organización Dep. Tecnol. Univ. Pompeu-Fabra, Barcelona, España
Revista 0214-1493
Publicación 2001, 45 (2): 477-527, 48 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain Ω' of the image is Jordan domain, a rectangle, for instance, and the image u Î C(Ω') ∩ WBV(Ω) (being constant near ∂Ω), we prove that for almost all levels λ of u, the classical connected components of positive measure of [u ≥ λ] coincide with the M-components of[ u ≥ λ]. Thus the notion of M-component can be seen as a relaxation ofthe classical notion of connected component when going from C(Ω') to WBV(Ω).
Clasificación UNESCO 120210 ; 121005
Palabras clave español Teoría de la medida ; Funciones de variación acotada ; Funciones de variable real ; Funciones continuas ; Mapa topográfico ; Teoría de Morse
Código MathReviews MR1876918
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