Displaying similar documents to “A note on the Lebesgue-Darst decomposition theorem.”

Lattice-valued Borel measures. III.

Surjit Singh Khurana (2008)

Archivum Mathematicum

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Let X be a completely regular T 1 space, E a boundedly complete vector lattice, C ( X ) ( C b ( X ) ) the space of all (all, bounded), real-valued continuous functions on X . In order convergence, we consider E -valued, order-bounded, σ -additive, τ -additive, and tight measures on X and prove some order-theoretic and topological properties of these measures. Also for an order-bounded, E -valued (for some special E ) linear map on C ( X ) , a measure representation result is proved. In case E n * separates...

Uniformly countably additive families of measures and group invariant measures.

Baltasar Rodríguez-Salinas (1998)

Collectanea Mathematica

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The extension of finitely additive measures that are invariant under a group permutations or mappings has already been widely studied. We have dealt with this problem previously from the point of view of Hahn-Banach's theorem and von Neumann's measurable groups theory. In this paper we construct countably additive measures from a close point of view, different to that of Haar's Measure Theory.

Representations of bimeasures

Kari Ylinen (1993)

Studia Mathematica

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Separately σ-additive and separately finitely additive complex functions on the Cartesian product of two algebras of sets are represented in terms of spectral measures and their finitely additive counterparts. Applications of the techniques include a bounded joint convergence theorem for bimeasure integration, characterizations of positive-definite bimeasures, and a theorem on decomposing a bimeasure into a linear combination of positive-definite ones.

Range of density measures

Martin Sleziak, Miloš Ziman (2009)

Acta Mathematica Universitatis Ostraviensis

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We investigate some properties of density measures – finitely additive measures on the set of natural numbers ℕ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence A ( n ) n as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of ℕ . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S.,...