The Fatou completion of a Fréchet function space and applications

Ricardo del Campo, Werner Ricker


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.



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

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Journal of the Austral. Maths Soc, copyright Australian Mathematical Society.