Isomorphically isometric probabilistic normed linear spaces.

Título inglés	Isomorphically isometric probabilistic normed linear spaces.
Título español	Espacios lineales normados probabilísticos isomórficamente isométricos.
Autor/es	Sherwood, Howard
Organización	Dep. Math. Stat. Univ. Central Florida, Orlando (Florida), Estados Unidos
Revista	0210-7821
Publicación	1979, 3 (2): 71-77, 3 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others. In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically generated if and only if it is isometric to an E-space. In this paper we extend these ideas and results to PNL spaces. We define E-norm spaces and pseudo-norm-generated PNL spaces and show that a PNL space is pseudo-norm-generated if and only if it is isomorphically isometric to an E-norm space. In order to preserve the algebraic structure in a meaningful way we require new constructions which differ considerably from those given in the original PM space setting.
Clasificación UNESCO	120225 ; 120804
Palabras clave español	Espacios normados ; Espacios probabilísticos ; Espacios métricos ; Isometría
Código MathReviews	MR0556648
Código Z-Math	Zbl 0432.60014
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