Displaying similar documents to “Integral representation of additive transformations on L p spaces”

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.

Decomposition of group-valued additive set functions

Tim Traynor (1972)

Annales de l'institut Fourier

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Let m be an additive function on a ring H of sets, with values in a commutative Hausdorff topological group, and let K be an ideal of H . Conditions are given under which m can be represented as the sum of two additive functions, one essentially supported on K , the other vanishing on K . The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.