On the Weak Sequential Completeness of the Spaces of Radon Measures

1985 ◽  
Vol 29 (1) ◽  
pp. 142-147 ◽  
Author(s):  
Yu. L. Daletskii ◽  
O. G. Smolyanov
Keyword(s):  
Radon Measures ◽  
Sequential Completeness

Invariant Radon measures and minimal sets for subgroups of Homeo+(R)

2020 ◽  
Vol 285 ◽  
pp. 107378
Author(s):  
Hui Xu ◽  
Enhui Shi ◽  
Yiruo Wang
Keyword(s):  
Radon Measures ◽  
Minimal Sets

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

Set-Theoretical Aspects and Radon Measures

1995 ◽  
pp. 177-288
Author(s):  
Bernd Anger ◽  
Claude Portenier
Keyword(s):  
Radon Measures

scholarly journals Sequential completeness of quotient groups

2000 ◽  
Vol 61 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Dikran Dikranjan ◽  
Michael Tkačenko
Keyword(s):  
Abelian Group ◽  
Direct Products ◽  
Topological Groups ◽  
Complete Group ◽  
Sequential Completeness ◽  
Algebraic Properties ◽  
Countable Compactness ◽  
Quotient Groups

We discuss various generalisations of countable compactness for topological groups that are related to completeness. The sequentially complete groups form a class closed with respect to taking direct products and closed subgroups. Surprisingly, the stronger version of sequential completeness called sequential h-completeness (all continuous homomorphic images are sequentially complete) implies pseudocompactness in the presence of good algebraic properties such as nilpotency. We also study quotients of sequentially complete groups and find several classes of sequentially q-complete groups (all quotients are sequentially complete). Finally, we show that the pseudocompact sequentially complete groups are far from being sequentially q-complete in the following sense: every pseudocompact Abelian group is a quotient of a pseudocompact Abelian sequentially complete group.

Daniell integral represented by Radon measures

1989 ◽  
Vol 38 (1) ◽  
pp. 39-59
Author(s):  
E. G. F. Thomas ◽  
A. Volčič
Keyword(s):  
Radon Measures
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