Measure Theory (eBook)
XVII, 1075 Seiten
Springer Berlin (Verlag)
978-3-540-34514-5 (ISBN)
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Vladimir Bogachev was born in Moscow in 1961. He got the PhD at Moscow State University in 1986 and he got the degree of Doctor of Sciences in 1990. Since 1986 Vladimir Bogachev has worked at the Department of Mechanics and Mathematics of Moscow State University. The main fields of his research are measure theory, nonlinear functional analysis, probability theory, and stochastic analysis. He is a well-nown expert in measure theory, probability theory, and the Malliavin calculus, and the author of more than 100 scientific publications. His monograph ``Gaussian Measures'' (AMS, 1998) has become a widely used source. Vladimir Bogachev hs been an invited speaker and a lecturer at many international conferences and several dozen universities and mathematical institutes over the world.
Scientific awards: a medal of the Academy of Sciences of the USSR and the Award of the Japan Society of Promotion of Science.
Vladimir Bogachev was born in Moscow in 1961. He got the PhD at Moscow State University in 1986 and he got the degree of Doctor of Sciences in 1990. Since 1986 Vladimir Bogachev has worked at the Department of Mechanics and Mathematics of Moscow State University. The main fields of his research are measure theory, nonlinear functional analysis, probability theory, and stochastic analysis. He is a well-nown expert in measure theory, probability theory, and the Malliavin calculus, and the author of more than 100 scientific publications. His monograph ``Gaussian Measures’’ (AMS, 1998) has become a widely used source. Vladimir Bogachev hs been an invited speaker and a lecturer at many international conferences and several dozen universities and mathematical institutes over the world. Scientific awards: a medal of the Academy of Sciences of the USSR and the Award of the Japan Society of Promotion of Science.
Preface 5
Contents 11
Contents of Volume 2 14
Constructions and extensions of measures 17
The Lebesgue integral 121
Operations on measures and functions 191
The spaces Lp and spaces of measures 265
Connections between the integral and 345
Connections between the integral and derivative 345
Bibliographical and Historical Comments 425
References 456
Subject Index 506
Preface to Volume 2 519
Contents 521
Contents of Volume 1 524
Borel, Baire and Souslin sets 527
Measures on topological spaces 593
Weak convergence of measures 701
Transformations of measures and isomorphisms 793
Conditional measures and conditional expectations 865
Bibliographical and Historical Comments 965
References 991
Subject Index 1087
Erscheint lt. Verlag | 15.1.2007 |
---|---|
Zusatzinfo | XVII, 1075 p. |
Verlagsort | Berlin |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
Technik | |
Schlagworte | convergence of measures • Derivative • differential equation • Lebesgue integral • linear optimization • measure • measure theory • MSC (2000). 28-00, 46GXX, 60-XX • Transformation • Transformation of mesures |
ISBN-10 | 3-540-34514-0 / 3540345140 |
ISBN-13 | 978-3-540-34514-5 / 9783540345145 |
Haben Sie eine Frage zum Produkt? |
![PDF](/img/icon_pdf_big.jpg)
Größe: 10,4 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Zusätzliches Feature: Online Lesen
Dieses eBook können Sie zusätzlich zum Download auch online im Webbrowser lesen.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich