Displaying similar documents to “A unified approach to Riesz type representation theorems”

Extensions of set functions.

Sergei V. Ovchinnikov, Jean Claude Falmagne (2003)

Mathware and Soft Computing

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We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is algo shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.

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.