On Repeated Sequential Closures of Constructible Functions in Valuations
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of the former space is equal to the latter one. This stronger property is necessary for some applications in Alesker (Geom Funct Anal 20(5):1073–1143, 2010).
KeywordsClosed Subspace Sequential Closure Linear Topological Space Constructible Function Generalize Valuation
I am very grateful to the anonymous referee for the careful reading of the first version of the paper and for numerous remarks.
Partially supported by ISF grant 1447/12.
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