Spaces of Measures 3110087847, 9783110087840

107 43

English Pages 448 [445] Year 1984

Spaces of Measures
3110087847, 9783110087840

Author / Uploaded
Corneliu Constantinescu

Table of contents :
Introduction
Logical connections between sections
Notations and Terminology
1. Set theory
2. Order relations
3. Topological spaces
4. Uniform spaces
Chapter 1: Topological preliminaries
1.1 Sets of filters
1.2 Sets of filters on topological and uniform spaces
1.3 .-continuous and uniformly .-continuous maps
1.4 Filters defined by sets of sequences
1.5 Sets of sequences on topological and uniform spaces
1.6 .-stable filters
1.7 Mioritic spaces
1.8 .i-continuous and uniformly .i-continuous maps
Chapter 2: Spaces of functions
2.1 Uniformities on spaces of functions
2.2 Uniformities on spaces of functions defined by sets of sequences
2.3 mulian spaces
2.4 Constructions with spaces of functions
2.5 Spaces of parametrized functions
Chapter 3: Spaces of supersummable families
3.1 The set G(I, G)
3.2 Structures on G (I, G)
3.3 Spaces of supersummable families
3.4 Spaces of supersummable families of functions
3.5 Supersummable families in special spaces
Chapter 4: Spaces of measures
4.1 Measures and exhaustive maps
4.2 Spaces of measures and of exhaustive additive maps
4.3 Vitali-Hahn-Saks theorem and Phillips lemma
4.4 Weak topologies on spaces of measures
4.5 Spaces of measures on topological spaces
4.6 Measures with parameter
4.7 Bounded sets
4.8 Bounded sets and measures on topological spaces
4.9 Spaces of integrals
4.10 Supersummable families of functions and their integrals
4.11 Measurability considerations
Chapter 5: Locally convex lattices
5.1 Order summable families
5.2 Order continuous maps
5.3 Spaces of order continuous group homomorphisms
5.4 Vector lattices
5.5 Duals of vector lattices
5.6 Spaces of vector valued measures
5.7 Quasi M-spaces
5.8 M-spaces
5.9 Strict M-spaces
References
Index
Notations

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