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Representations of bimeasures. (English) Zbl 0809.28001

Summary: Separately \(\sigma\)-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.

MSC:

28A10 Real- or complex-valued set functions
46L05 General theory of \(C^*\)-algebras
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