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Sigma-finiteness and regularity of generalized Radon measures.

J. Fernández Novoa (1990)

Collectanea Mathematica

We extend some known sigma-finiteness and regularity results for (locally finite) Radon measures to locally sigma-finite or locally moderated Radon measures of type (H), and we obtain other new ones. The main result states that the regularity and the sigma-finiteness are equivalent for alllocally moderated, diffused, Radon measures of type (H) in a T1 topological space which is either weakly metacompact or paralindelöf (resp. metalindelöf) and has a concassage of Lindelöf (resp. separable) subsets....

Some problems for measures on non-standard algebraic structures

Maria Gabriella Graziano (2000)

Bollettino dell'Unione Matematica Italiana

Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...

Strict topologies as topological algebras

Surjit Singh Khurana (2001)

Czechoslovak Mathematical Journal

Let X be a completely regular Hausdorff space, C b ( X ) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m -convex.

Strong Fubini axioms from measure extension axioms

Piotr Zakrzewski (1992)

Commentationes Mathematicae Universitatis Carolinae

It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.

Structure of measures on topological spaces.

José L. de María, Baltasar Rodríguez Salinas (1989)

Revista Matemática de la Universidad Complutense de Madrid

The Radon spaces of type (T), i.e., topological spaces for which every finite Borel measure on Omega is T-additive and T-regular are characterized. The class of these spaces is very wide and in particular it contains the Radon spaces. We extend the results of Marczewski an Sikorski to the sygma-metrizable spaces and to the subsets of the Banach spaces endowed with the weak topology. Finally, the completely additive families of measurable subsets related with the works of Hansell, Koumoullis, and...

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