On the Nakano Individual Convergence

  • R. Zaharopol

    Binghamton University, USA


We have recently defined the notion of individual convergence for a sequence of positive elements of an Archimedean Riesz space . In the note we complete the definition (i.e., we define the individual convergence for sequences of not necessarily positive elements of ), and we prove that our notion of individual convergence is a natural extension of the individual convergence as defined by Nakano: we will prove that if a sequence of elements of has an individual limit in the Nakano sense, then it converges individually with respect to our definition.

Cite this article

R. Zaharopol, On the Nakano Individual Convergence. Z. Anal. Anwend. 13 (1994), no. 2, pp. 181–189

DOI 10.4171/ZAA/517