Full paper in PDF:
$%S. Díaz, A. Fernández, M. Florencio, and P. J. Paúl, The space of countably simple bounded functions with values in a DF-space, Rev. Mat. Univ. Complut. Madrid 7 (1994), no. 2, 219–232.%$

The Space of Countably Simple Bounded Functions with Values in a DF-space

Santiago DíAZ, Antonio FERNÁNDEZ LÓPEZ,
Miguel FLORENCIO, and Pedro J. PAÚL

E.S. Ingenieros Industriales
Avda. Reina Mercedes s/n
41012 Sevilla — Spain

Received: January 7, 1993
Revised: June 1, 1993

ABSTRACT

We study the possibility of lifting some properties, as being a (barreled, quasi-barreled, bornological, or ultrabornological) DF, gDF, or quasi-normable space, from a locally convex space $E$ to the space $S ,\ 0(m,E)$ , of countably-valued and bounded (classes of $m$ -a.e. equal) functions from a measure space $(_O_,S,m)$ into $E$ .

1991 Mathematics Subject Classification: 46A04, 46A08, 46E30, 46E40.