Measure and Integration Theory

Copertina anteriore
Walter de Gruyter, 20 apr 2011 - 246 pagine

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Titles in planning include

Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo, Periodic Locally Compact Groups: A Study of a Class of Totally Disconnected Topological Groups (2018)
Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2018)
Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019)
Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)
Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press)
Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020)
Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021)
Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021)
Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)
Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

 

Pagine selezionate

Sommario

Chapter I Measure Theory
1
1 σalgebras and their generators
2
2 Dynkin systems
5
3 Contents premeasures measures
8
4 Lebesgue premeasure
14
5 Extension of a premeasure to a measure
18
6 LebesgueBorel measure and measures on the number line
26
7 Measurable mappings and image measures
34
19 Integration with respect to an image measure
110
20 Stochastic convergence
112
21 Equiintegrability
121
Chapter III Product Measures
132
23 Product measures and Fubinis theorem
135
24 Convolution of finite Borel measures
147
Chapter IV Measures on Topological Spaces
152
26 Radon measures on Polish spaces
157

8 Mapping properties of the LebesgueBorel measure
38
Chapter II Integration Theory
49
10 Elementary functions and their integral
53
11 The integral of nonnegative measurable functions
57
12 Integrability
64
13 Almost everywhere prevailing properties
70
14 The spaces Lpμ
74
15 Convergence theorems
79
16 Applications of the convergence theorems
88
the RadonNikodym theorem
96
18 Signed measures
107
27 Properties of locally compact spaces
166
28 Construction of Radon measures on locally compact spaces
170
29 Riesz representation theorem
177
30 Convergence of Radon measures
188
31 Vague compactness and metrizability questions
204
Bibliography
217
Symbol Index
221
Name Index
223
Subject Index
225
Copyright

Altre edizioni - Visualizza tutto

Measure and Integration Theory
Heinz Bauer
Anteprima limitata - 2001

Parole e frasi comuni

A₁ A₂ arbitrary Borel measure Borel sets cach called Ce(E compact sets compact subset Consequently consider continuous converges in pth Corollary countable base d-dimensional defined definition denote disjoint sets Dynkin system equality equi-integrable equivalent Example Exercise exists finite measure follows function f ƒ and g ƒ dµ ƒ ƒ hypothesis indicator function inequality inner regular interval isotone isotone sequence L-B measure Lemma lim inf lim sup locally compact space mapping measurable function measurable numerical functions measurable real function measure space measure µ metric N₂ non-negative nullset numerical measure o-additivity o-algebra o-finite open sets outer regular p-fold integrable p-measure pairwise disjoint sets Polish space positive linear form premeasure properties prove pth mean Radon measure real numbers real-valued relatively compact Remark representing measure resp respect satisfies sequence fn Show stochastic convergence theory u-integrable union vague topology vaguely convergent w₁ µ(An

Informazioni sull'autore (2011)

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

Informazioni bibliografiche

TitoloMeasure and Integration Theory
Volume 26 di De Gruyter Studies in Mathematics
AutoreHeinz Bauer
tradotto daRobert B. Burckel
EditoreWalter de Gruyter, 2011
ISBN311086620X, 9783110866209
Lunghezza246 pagine
  
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