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Topological rings of sets and the theory of vector measures

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Bogdan V. M., Oberle R. A.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction............................................................................................................................................................... 5 Chapter I. Topological rings of sets 1.1. Definition and basic properties of topological rings of sets............................................................... 7 1.2. Topological rings of sets generated by Rickart families of contents................................................ 12 Chapter II. The space of Rickart vector charges on a ring of sets 2.1. Definition and basic properties of Rickart vector charges................................................................... 23 2.2. Pointwise convergent sequences of Rickart vector charges.............................................................. 28 Chapter III. Equicontinuous sequences of Rickart vector charges 3.1. Vectorial generalizations of the Nikodym boundedness theorem..................................................... 35 3.2. Generalizations of the Vitali-Hahn-Saks theorem................................................................................. 39 Chapter IV. Weak compactness and decompositions of strongly bounded vector charges 4.1. Weak compactness in the spaces of finitely additive scalar charges on an algebra of sets................................................................................................................................................ 42 4.2. Decompositions of strongly bounded vector charges.......................................................................... 45 Chapter V. Extensions of Rickart vector measures 5.1. Extensions of countably additive Rickart vector measures.................................................................. 52 5.2. General extension of vector measures.................................................................................................... 55 Summary of definitions............................................................................................................................................ 67 References................................................................................................................................................................. 68

Ograniczanie wyników

1 Bogdan V. M.

1 Oberle R. A.

1 1978

Wyniki wyszukiwania

Topological rings of sets and the theory of vector measures