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THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS
Part of
R. DEL CAMPO, W. J. RICKER
Journal:

Journal of the Australian Mathematical Society / Volume 88 / Issue 1 / February 2010

Published online by Cambridge University Press:

08 December 2009, pp. 49-60

Print publication:

February 2010
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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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THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS