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THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS
Published online by Cambridge University Press: 08 December 2009
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 L1(ν) of integrable functions with respect to a Fréchet-space-valued measure ν is the space L1w(ν) of scalarly ν-integrable functions. Further consequences are also given.
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- Copyright © Australian Mathematical Publishing Association Inc. 2009
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