THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS
2009 ◽
Vol 88
(1)
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pp. 49-60
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Keyword(s):
AbstractGiven 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.
2009 ◽
Vol 354
(2)
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pp. 641-647
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1975 ◽
Vol 27
(5)
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pp. 1110-1113
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1972 ◽
Vol 6
(2)
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pp. 161-167
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Keyword(s):
1974 ◽
Vol 26
(6)
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pp. 1294-1300
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Keyword(s):
2013 ◽
Vol 2013
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pp. 1-6
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2018 ◽
Vol 13
(01)
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pp. 2050017
Keyword(s):
1981 ◽
Vol 82
(4)
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pp. 655-655
Keyword(s):
1990 ◽
Vol 13
(3)
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pp. 607-610
Keyword(s):
1996 ◽
Vol 120
(3)
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pp. 489-498
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Keyword(s):