Bernard R. Gelbaum 
Modern Real and Complex Analysis [PDF ebook] 

Modern Real and Complex Analysis

Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum’s approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman’s kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.

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REAL ANALYSIS.

Fundamentals.

Integration.

Functional Analysis.

More Measure Theory.

COMPLEX ANALYSIS.

Locally Holomorphic Functions.

Harmonic Functions.

Meromorphic and Entire Functions.

Conformal Mapping.

Defective Functions.

Riemann Surfaces.

Convexity and Complex Analysis.

Several Complex Variables.

Bibliography.

Symbol List.

Glossary/Index.

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BERNARD R. GELBAUM is Professor of Mathematics at the State University of New York at Buffalo. He has previously served on the faculties of the University of Minnesota, the University of California, Irvine, and as a Fulbright Senior Scholar at University College, Galway, Ireland. He has published research in analysis and probability theory and is the author of Theorems and Counterexamples in Mathematics; Problems in Real and Complex Analysis; and Linear Algebra: Basics, Practice and Theory.