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On measure zero sets in topological vector spaces. (English) Zbl 0862.28002
By an application of Fubini’s theorem it is shown that there exists a probability measure on the Borel subsets of an $$F$$-space in the sense of W. Rudin vanishing for all zero sets in the sense of Aronszajn. In particular, non-empty open subsets of a separable $$F$$-space are not zero sets in the sense of Aronszajn.
##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) 46G12 Measures and integration on abstract linear spaces
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