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
@book{bwmeta1.element.zamlynska-e5e80241-2aa9-482a-8a8b-0c1b2ed7f299,
author = {V. M. Bogdan and R. A. Oberle},
title = {Topological rings of sets and the theory of vector measures},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1978},
zbl = {0386.28010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-e5e80241-2aa9-482a-8a8b-0c1b2ed7f299}
}
V. M. Bogdan; R. A. Oberle. Topological rings of sets and the theory of vector measures. GDML_Books (1978), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-e5e80241-2aa9-482a-8a8b-0c1b2ed7f299/