Measure Theory (Graduate Texts in Mathematics, 18)

Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWS

Science & Math

Halmos, Paul R.

Mathematics

Springer

Naive Set Theory (University Series in Undergraduate Mathematics)

D.Van Nostrand

Hilbert Space Problem Book 1ST Edition by Paul Halmos (Author) (9.25x6.3x1.3in 365pgs Hardcover NO DJ) D VAN NOSTRAND COMPANY INC (1967)

A Hilbert Space Problem Book

This book "Naive Set Theory" uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know... Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics.

Naive Set Theory

Reference

Blurb

Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Algebraic Logic (Dover Books on Mathematics)

Dover Publications

A fine example of a great mathematician's intellect and mathematical style, this classic on linear algebra is widely cited in the literature. The treatment is an ideal supplement to many traditional linear algebra texts and is accessible to undergraduates with some background in algebra. "This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations … It's also extremely well-written and logical, with short and elegant proofs. … The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis … and a brief summary of what is needed to extend this theory to Hilbert spaces." — Allen Stenger, MAA Reviews, maa.org, May, 2016. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other 'modern' textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well-placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." — Zentralblatt für Mathematik.

Finite-Dimensional Vector Spaces: Second Edition (Dover Books on Mathematics)

This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters. "This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics." — Allen Stenger, The Mathematical Association of America, September 2011.

Naive Set Theory (Dover Books on Mathematics)

This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

Lectures on Ergodic Theory (Dover Books on Mathematics)

This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. Author Paul R. Halmos notes in the Preface that his motivation in writing this text was to make available to a wider audience the results of the third chapter, the so-called multiplicity theory. The theory as he presents it deals with arbitrary spectral measures, including the multiplicity theory of normal operators on a not necessarily separable Hilbert space. His explication covers, as another useful special case, the multiplicity theory of unitary representations of locally compact abelian groups. Suitable for advanced undergraduates and graduate students in mathematics, this volume's sole prerequisite is a background in measure theory. The distinguished mathematician E. R. Lorch praised the book in the Bulletin of the American Mathematical Society as "an exposition which is always fresh, proofs which are sophisticated, and a choice of subject matter which is certainly timely."

Introduction to Hilbert Space and the Theory of Spectral Multiplicity: Second Edition (Dover Books on Mathematics)

Chemistry

This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.

Lectures on Boolean Algebras (Dover Books on Mathematics)

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Books by Halmos, Paul R.