Examples of ε-exhaustive pathological submeasures
نویسندگان
چکیده
منابع مشابه
Examples of Ε-exhaustive Pathological Submeasures
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...
متن کاملPathological Linear Spaces and Submeasures
Let K be a compact Hausdorff space and let )~ be a probability measure on K. We denote by Lo(K,2) the space of all Borel functions f:K--*N with the topology of convergence in measure. Lo(K, 2) is an F-space (complete metric topological vector space) if, as usual, we identify functions equal almost everywhere. Spaces of the type Lo(K,2 ) are probably the most studied examples of non-locally conv...
متن کاملUniformly 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.
متن کاملExamples of Entire Functions with Pathological Dynamics
The basic results of the iteration theory of rational and entire functions used in this paper are contained in the classical papers [10,11], in the survey [5] and in [15, Appendix III]. Let / b e a rational or entire function and let/" = /o . . . o /be its «th iterate. Denote by Jf(f) the set of normality of/ that is, the maximal open set on which the family of iterates is normal in the sense o...
متن کاملSome pathological examples of precipitous ideals
We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [1] and R. Laver [4] respectively. The present examples differ in two ways: firstthey use only a measurable cardinal and secondthe ideals are over a cardinal. Also a precipitous ideal without a norm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2004
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm181-3-4