Uniformly Exhaustive Submeasures and Nearly Additive Set Functions
نویسندگان
چکیده
Every uniformly exhaustive submeasure is equivalent to a measure. From this, we deduce that every vector measure with compact range in an F-space has a control measure. We also show that co (or any E.-space) is a T;space, i.e. cannot be realized as the quotient of a nonlocally convex F-space by a one-dimensional subspace.
منابع مشابه
Remarks on measurable Boolean algebras and sequential cardinals
The paper offers a generalization of Kalton–Roberts’ theorem on uniformly exhaustive Maharam’s submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.
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