HomeGroupsTalkMoreZeitgeist
Search Site
This site uses cookies to deliver our services, improve performance, for analytics, and (if not signed in) for advertising. By using LibraryThing you acknowledge that you have read and understand our Terms of Service and Privacy Policy. Your use of the site and services is subject to these policies and terms.

Results from Google Books

Click on a thumbnail to go to Google Books.

Loading...

A Concise Introduction to the Theory of Integration

by Daniel W. Stroock

MembersReviewsPopularityAverage ratingConversations
18None1,184,285 (4)None
The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of LEBESGUE's measure for (RN and eye toward applications to real analysis and probability theory. Following a brief review of the classical RIEMANN theory in Chapter I, the details of LEBESGUE's construction are given in Chapter II, which also contains a derivation of the transformation properties of LEBESGUE's measure under linear maps. Chapter III is devoted to LEBESGUE's theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and FUBINI's Theorem. In Chapter IV, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of RIEMANN integrals with respect to the distribution function, polar coordinates, JACOBI's transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of JENSEN, MINKOWSKI and H LDER are presented. Finally, Chapter VI starts with the DANIELL integral and its applications to the CARATH ODORY Extension and RIESZ Representation Theorems. It closes with VON NEUMANN's derivation of the RADON-NIKODYM Theorem.… (more)
None
Loading...

Sign up for LibraryThing to find out whether you'll like this book.

No current Talk conversations about this book.

No reviews
no reviews | add a review

Belongs to Series

You must log in to edit Common Knowledge data.
For more help see the Common Knowledge help page.
Canonical title
Original title
Alternative titles
Original publication date
People/Characters
Important places
Important events
Related movies
Epigraph
Dedication
First words
Quotations
Last words
Disambiguation notice
Publisher's editors
Blurbers
Original language
Canonical DDC/MDS
Canonical LCC

References to this work on external resources.

Wikipedia in English

None

The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of LEBESGUE's measure for (RN and eye toward applications to real analysis and probability theory. Following a brief review of the classical RIEMANN theory in Chapter I, the details of LEBESGUE's construction are given in Chapter II, which also contains a derivation of the transformation properties of LEBESGUE's measure under linear maps. Chapter III is devoted to LEBESGUE's theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and FUBINI's Theorem. In Chapter IV, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of RIEMANN integrals with respect to the distribution function, polar coordinates, JACOBI's transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of JENSEN, MINKOWSKI and H LDER are presented. Finally, Chapter VI starts with the DANIELL integral and its applications to the CARATH ODORY Extension and RIESZ Representation Theorems. It closes with VON NEUMANN's derivation of the RADON-NIKODYM Theorem.

No library descriptions found.

Book description
Haiku summary

Current Discussions

None

Popular covers

Quick Links

Rating

Average: (4)
0.5
1
1.5
2
2.5
3
3.5
4 1
4.5
5

Is this you?

Become a LibraryThing Author.

 

About | Contact | Privacy/Terms | Help/FAQs | Blog | Store | APIs | TinyCat | Legacy Libraries | Early Reviewers | Common Knowledge | 203,226,798 books! | Top bar: Always visible