The Fatou completion of a Fréchet function space and applications

Ricardo del Campo, Werner Ricker

Abstract


Given a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space $L^1(\nu)$ of integrable functions with respect to a Fréchet-space-valued measure $\nu$ is the space $L^1_w(\nu)$ of scalarly $\nu$-integrable functions. Further consequences are also given.

doi:10.1017/S1446788709000238

Keywords


Fréchet space (lattice), vector measure, Fatou property, Lebesgue topology, scalarly integrable function



If you have difficultly logging in, then clear your browser cache, restart your browser, and try again. In October we upgraded this online system and hence some of your old cookies need to be renewed.

Remember for most actions you have to record/upload into OJS and then inform the editor/author via clicking on an email icon or Completion button.
Journal of the Austral. Maths Soc, copyright Australian Mathematical Society.