zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Measures, integrals and martingales. (English) Zbl 1084.28001
Cambridge: Cambridge University Press (ISBN 0-521-61525-9/pbk; 0-521-85015-0/hbk). x, 381 p. £ 24.95, $ 50.00/pbk; £ 50.00, $ 90.00/hbk (2005).
The present book is an elementary but thorough introduction to a wide variety of first year graduate level topics in analysis including the Lebesgue integral, abstract measure theory, and associated theorems such as the Fubini-Tonelli theorem, and the Jacobi transformation theorem for integrals. The topics also lay the foundation for advanced probability theory by introducing filtered measure spaces, associated martingales, and convergence theorems with application to the Raydon-Nikodým theorem.\par\noindent The author includes an introduction to many other topics that might be found in a standard functional analysis course such as Hilbert spaces, the uniform boundedness principle, and orthogonal systems.\par\noindent This book should be accessible to anyone with a strong undergraduate background in calculus, linear algebra, and real analysis.

28-01Textbooks (measure and integration)
28A60Measures on Boolean rings, measure algebras
28A33Spaces of measures, convergence of measures
28A35Measures and integrals in product spaces
Full Text: DOI