Based on the authors' courses and lectures, this two-part advanced-level
text is now available in a single volume. Topics include metric and
normed spaces, continuous curves in metric spaces, measure theory,
Lebesque intervals, Hilbert space, and more. Each section contains
exercises. Lists of symbols, definitions, and theorems. 1957 edition.
This book is meant as a text for a first-year graduate course in
analysis. In a sense, it covers the same topics as elementary calculus
but treats them in a manner suitable for people who will be using it in
further mathematical investigations. The organization avoids long chains
of logical interdependence, so that chapters are mostly independent.
This allows a course to omit material from some chapters without
compromising the exposition of material from later chapters.
This classic text is written for graduate courses in functional
analysis. This text is used in modern investigations in analysis and
applied mathematics. This new edition includes up-to-date presentations
of topics as well as more examples and exercises. New topics include
Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem,
and an ergodic theorem. 