Topological rings of sets and the theory of vector measures

V. M. Bogdan, and R. A. Oberle. Topological rings of sets and the theory of vector measures. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1978. <http://eudml.org/doc/268597>.

@book{V1978,
abstract = {CONTENTSIntroduction............................................................................................................................................................... 5Chapter 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................................................ 12Chapter 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.............................................................. 28Chapter 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................................................................................. 39Chapter 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.......................................................................... 45Chapter V. Extensions of Rickart vector measures 5.1. Extensions of countably additive Rickart vector measures.................................................................. 52 5.2. General extension of vector measures.................................................................................................... 55Summary of definitions............................................................................................................................................ 67References................................................................................................................................................................. 68},
author = {V. M. Bogdan, R. A. Oberle},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Topological rings of sets and the theory of vector measures},
url = {http://eudml.org/doc/268597},
year = {1978},
}

TY - BOOK
AU - V. M. Bogdan
AU - R. A. Oberle
TI - Topological rings of sets and the theory of vector measures
PY - 1978
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction............................................................................................................................................................... 5Chapter 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................................................ 12Chapter 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.............................................................. 28Chapter 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................................................................................. 39Chapter 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.......................................................................... 45Chapter V. Extensions of Rickart vector measures 5.1. Extensions of countably additive Rickart vector measures.................................................................. 52 5.2. General extension of vector measures.................................................................................................... 55Summary of definitions............................................................................................................................................ 67References................................................................................................................................................................. 68
LA - eng
UR - http://eudml.org/doc/268597
ER -