Uniformly exhaustive submeasures and nearly additive set functions
نویسندگان
چکیده
منابع مشابه
Uniformly Exhaustive Submeasures and Nearly Additive Set Functions
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.
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A submeasure θ on a Boolean algebra B is pathological if it does not dominate a positive finitely additive functional. It is ε-exhaustive if every sequence {An} of pairwise disjoint sets in B satisfies lim supn θ(An) ≤ ε. It is exhaustive if it is 0-exhaustive. It is normalized if θ(1B) = 1. Question 1. Is there a normalized exhaustive pathological submeasure on the algebra of clopen subsets of...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1983
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1983-0701524-4