Measure and Integration Theory

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Walter de Gruyter, 2001 - 230 pagine

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Sommario

Measure Theory 125
1
Dynkin systems
6
Contents premeasures measures
8
Lebesgue premeasure
14
Extension of a premeasure to a measure
18
LebesgueBorel measure and measures on the number line
26
Measurable mappings and image measures
34
Mapping properties of the LebesgueBorel measure
38
Signed measures
107
Integration with respect to an image measure
110
Stochastic convergence
112
Equiintegrability
121
Product Measures
132
Product measures and Fubinis theorem
135
Convolution of finite Borel measures
147
Measures on Topological Spaces
152

Integration Theory
49
Elementary functions and their integral
53
The integral of nonnegative measurable functions
57
Integrability
64
Almost everywhere prevailing properties
70
The spaces LP
74
Convergence theorems
79
Applications of the convergence theorems
88
the RadonNikodym theorem
96
Radon measures on Polish spaces
157
Properties of locally compact spaces
166
Construction of Radon measures on locally compact spaces
170
Riesz representation theorem
177
Convergence of Radon measures
188
Vague compactness and metrizability questions
204
Bibliography
217
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Informazioni sull'autore (2001)

Professor Heinz Bauer (1928--2002) was Professor at the Mathematical Institute of the Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Germany.

Informazioni bibliografiche