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1. Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos | |
Hardcover: 324
Pages
(1974-01-01)
list price: US$64.95 -- used & new: US$44.99 (price subject to change: see help) Asin: 0387900888 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
An excellent introduction to measure theory
Measure Theory -- where are the axioms??
A classic in the field The next chapter explores more carefully the relation between measures and outer measures. It is also shown in this chapter to what extent a measure on a ring can be extended to the generated sigma-ring. The all-important Lebesgue measure is developed here also, and the author exhibits an example of a non-measurable set. In order to develop an integration theory, one must first characterize the collection of measurable functions, and the author does this in chapter 4. The convergence properties of measurable functions are carefully outlined by the author. The theory of integration begins in chapter 5, wherein the author follows the standard construction of an integral by first defining integrals over simple functions. Then in chapter 6, signed measures are defined, and the Lebesgue bounded convergence theorem is proven and the Hahn and Jordan decompositions of these measures are discussed. The all-important Radon-Nikodym theorem, which gives an integral representation of an absolutely continuous sigma-finite signed measure, is proven in detail. One can of course take the Cartesian product of two measurable spaces, and the author shows how to define measures on these products in chapter 7, including infinite products. The physicist reader may want to pay attention to the section on infinite dimensional product measures, as it does have applications to functional integration in quantum field theory (although somewhat weakly). The author treats measurable transformations in chapter 8, but interestingly, the word "ergodic" is never mentioned. He also introduces briefly the L-p spaces, so very important in many areas of mathematics, and proves the Holder and Minkowski inequalities. The next chapter is the most important in the book, for it covers the notion of probability on measure spaces. After an brief motivation in the first section of the chapter, probability spaces are defined, and Bayes' theorem is discussed as an exercise. Both the weak and strong law of large numbers is proven in detail. Things get more abstract in chapter 10, which discusses measure theory on locally compact spaces. Borel and Baire sets on these kinds of spaces are defined, and the author gives detailed arguments on what must be changed when doing measure theory in this more general kind of space. The book ends with a discussion of measure theory on topological groups via the Haar measure. This chapter also has connections to physics, such as in the Faddeev-Popov volume measure over gauge equivalent classes in quantum field theory. The author does a fine job of characterizing the important properties of the Haar measure.
an excellent book |
2. I Want to Be a Mathematician: An Automathography by P.R. Halmos | |
Hardcover: 444
Pages
(1985-05-17)
list price: US$64.95 -- used & new: US$53.45 (price subject to change: see help) Asin: 0387960783 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
Wonderful look at mathematics, the times & the author |
3. PAUL HALMOS Celebrating 50 Years of Mathematics | |
Hardcover: 320
Pages
(1991-05-20)
list price: US$99.00 -- used & new: US$65.00 (price subject to change: see help) Asin: 0387975098 Canada | United Kingdom | Germany | France | Japan | |
4. Linear Algebra Problem Book by Paul Halmos | |
Paperback:
Pages
(2009-01-01)
Asin: B002OL0TLS Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (6)
Text is great, printing is not
Not as good for second year graduate students
Great book!
Start out with one of the best
Clear, interesting, easy to follow. |
5. Introduction to Boolean Algebras by Steven Givant | |
Kindle Edition: 588
Pages
(1966-11-30)
list price: US$59.95 Asin: B003T0GUHK Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book is an informal, although systematic presentation of lectures given by the authors on Boolean algebras, intended for advanced undergraduates and beginning graduate students. In a bold and refreshing style, this book treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled throughout the text for course study. This bookÂ can be considered a sequel to Paul Halmos's Lectures on Boolean Algebras, with the following changes: (1) the material in every section has been explained in more detail, and is now more accessible to undergraduates; (2) there are three times as many exercises, and the authors have now prepared a solutions manual; (3) a more careful explanation of the relationship between Boolean rings and Boolean algebras has been added; (4) thirteen chapters have been added, including chapters on topology and on continuous functions, a chapter on the extension theorem for homomorphisms, a new chapter on congruences and quotient algebras, a chapter on the lattice of ideals, and a chapter on duality theory for products. Customer Reviews (2)
Superb introduction. (Contains one flaw.) Some people draw a sharp distinction between the concepts of "Boolean space" (a totally disconnected compact Hausdorff space) and "Stone space", the difference being that a Stone space is the Stone space _of_ a Boolean algebra. A Boolean algebra's Stone space is the space of all of its 2-valued homomorphisms with the topology of pointwise convergence of nets of such homomorphisms. That every Boolean space is the Stone space of some Boolean algebra (namely, the Boolean algebra of all of its clopen subsets) is one of the important facts of "Stone's duality". Halmos never mentions the phrase "Stone space", but he proves the basic facts about "Stone's duality": that the category of Boolean algebras and Boolean homomorphisms is the opposite of the category of Boolean spaces and continuous functions. The flaw is in Lecture 21. Much of that section is founded upon an error -- that a Boolean algebra may have various non-isomorphic completions, of which one is "minimal". A careful mathematician can reconstruct that lecture and get much that is of value, but some may be unfortunately misled. One other thing irritates me: Halmos uses the word "non-atomic" rather than the much better term "atomless". The problem with "non-atomic" is that it may be mistaken for "not atomic", and that is a quite different thing. This book is now out of print. I'd like to see Dover reprint it.
ONE OF THE BEST |
6. Logic as Algebra (Dolciani Mathematical Expositions) by Paul Halmos, Steven Givant | |
Paperback: 151
Pages
(1998-09-03)
list price: US$36.00 -- used & new: US$30.60 (price subject to change: see help) Asin: 0883853272 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
A superb introduction to the glories of Boolean algebra
A Builder of a Solid Foundation in Mathematics Published in Smarandache Notions Journal reprinted withpermission. ... Read more |
7. Finite-Dimensional Vector Spaces (University series in Undergraduate Mathematics) by Paul R. Halmos | |
Hardcover: 200
Pages
(1958-01-01)
Asin: B000QA7SZ4 Canada | United Kingdom | Germany | France | Japan | |
8. A Glimpse at Hilbert Space Operators: Paul R. Halmos in Memoriam (Operator Theory: Advances and Applications) | |
Hardcover: 362
Pages
(2010-08-11)
list price: US$179.00 -- used & new: US$143.19 (price subject to change: see help) Asin: 3034603460 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The book is a commemorative volume honoring the mathematician Paul R. Halmos (1916-2006), who contributed passionately to mathematics in manifold ways, among them by basic research, by unparalleled mathematical exposition, by unselfish service to the mathematical community, and, not least, by the inspiration others found in his dedication to that community.Halmos made fundamental contributions in several areas of mathematics. This volume emphasises Halmos's contributions to operator theory, his venue for most of his mathematical life. The core of the volume is a series of expository articles by prominent operator theorists providing an overview of how operator theory prospered during the Halmos era, in no small measure thanks to Halmos's leadership and penetrating insights. |
9. Lectures on Ergodic Theory (AMS Chelsea Publishing) by Paul R. Halmos | |
Hardcover: 99
Pages
(2006-04-30)
list price: US$25.00 -- used & new: US$19.99 (price subject to change: see help) Asin: 0821841254 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A Clear Exposition of Ergodic Theory |
10. Finite Dimensional Vector Spaces. (AM-7) (Annals of Mathematics Studies) by Paul R. Halmos | |
Paperback: 196
Pages
(1947-01-01)
list price: US$46.95 -- used & new: US$41.66 (price subject to change: see help) Asin: 0691090955 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (15)
I got the book itself in great condition, BUT
Amazing.
Linear Algebra Bible
Good Reading.
A Classic for the mathematically-inclined.Good preparation for learning quantum mechanics. |
11. I Have a Photographic Memory by Paul R. Halmos | |
Paperback: 326
Pages
(1987-06-01)
list price: US$45.00 -- used & new: US$45.00 (price subject to change: see help) Asin: 0821819399 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
12. The sociology of mass-media communicators (The Sociological review monograph) by Paul Halmos | |
Paperback: 248
Pages
(1969)
Isbn: 0900770007 Canada | United Kingdom | Germany | France | Japan | |
13. The Faith of the Counsellors; A Study in the Theory and Practice of Social Case Work and Psychotherapy by Paul Halmos | |
Hardcover: 220
Pages
(1966)
Asin: B0006D658C Canada | United Kingdom | Germany | France | Japan | |
14. Readings in General Psychology | |
Hardcover: 262
Pages
(1959-12)
Isbn: 0710014864 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
15. The sociology of science (The Sociological review monograph) by Paul Halmos | |
Paperback: 226
Pages
(1972)
Asin: B0006CAXDG Canada | United Kingdom | Germany | France | Japan | |
16. Faith of the Counsellors by Paul R Halmos | |
Paperback:
Pages
(1979)
Asin: B0041URXPU Canada | United Kingdom | Germany | France | Japan | |
17. Sociological Review Monograph #6: THE CANFORD FAMILIES: A Study in Social Casework and Group Work by Paul (ed) Halmos | |
Hardcover:
Pages
(1962)
Asin: B0041QB666 Canada | United Kingdom | Germany | France | Japan | |
18. Measure Theory by Paul R. Halmos | |
Hardcover:
Pages
(1959)
Asin: B000NW80B6 Canada | United Kingdom | Germany | France | Japan | |
19. Sociology of Sociology (Sociological Review Monograph) | |
Hardcover: 179
Pages
(1970-09)
Isbn: 0900770120 Canada | United Kingdom | Germany | France | Japan | |
20. Solitude and Privacy: A Study of Social Isolation, its Causes and Therapy (International Library of Sociology) by Paul Halmos | |
Hardcover: 200
Pages
(2003-01-31)
list price: US$360.00 -- used & new: US$288.00 (price subject to change: see help) Asin: 0415177979 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Originally published in 1952. |
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