Adjoint spaces of abstract spaces
Porcelli, Pasquale (1966)
Portugaliae mathematica
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Porcelli, Pasquale (1966)
Portugaliae mathematica
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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.
L. Drewnowski (1973)
Studia Mathematica
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Utpal Bandyopadhyay (1973)
Studia Mathematica
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Javier Peralta (1984)
Collectanea Mathematica
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K. Sundaresan (1969)
Studia Mathematica
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Robert Freud (1980)
Acta Arithmetica
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James E. Huneycutt Jr. (1971)
Annales de l'institut Fourier
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In 1955, A. Revuz - Annales de l’Institut Fourier, vol. 6 (1955-56) - considered a type of Stieltjes measure defined on analogues of half-open, half-closed intervals in a partially ordered topological space. He states that these functions are finitely additive but his proof has an error. We shall furnish a new proof and extend some of this results to “measures” taking values in a topological abelian group.
I. Kátai (1977)
Colloquium Mathematicae
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W. Narkiewicz (1974)
Colloquium Mathematicae
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Stanisław Saks
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CONTENTS PREFACE...................... III ERRATA.......................... VII CHAPTER I. The integral in an abstract space § 1. Introduction.................................. 1 § 2. Terminology and notation...................... 4 § 3. Abstract space X.............................. 6 § 4. Additive classes of sets...................... 7 § 5. Additive functions of a set................... 8 § 6. The variations of an additive function........ 10 § 7. Measurable functions.............................